# 有限群的Cauchy定理基礎 · 脈衝 R01

本批已通過 Schema、去重、來源快照與獨立答案重算；仍未標記為人工審定。

本題庫已有對應的中英逐步詳解。原題的 candidate 與英文 ai_candidate 狀態保留；AI 覆核、有限計算與 Lean 形式證明分開標示。

batch-20261014-advance-20261112-r01-cauchy-theorem-finite-groups-foundations · 2026-10-14 · 100 題

欄序為來源綁定的呈現補充；原始 JSONL 與數學答案不變。

[欄序與來源綁定資料](https://ocme.evemisslab.com/data/i18n/question-output-protocols.json)



## 1. 有限群的Cauchy定理

完整有限群、prime divisor與exact element-order證書。操作=cauchy-prime-divisor-qualification；資料={"group_table":[[0,1,2,3,4,5],[1,2,3,4,5,0],[2,3,4,5,0,1],[3,4,5,0,1,2],[4,5,0,1,2,3],[5,0,1,2,3,4]],"identity":0,"prime":2}。請依 [group_order, prime, qualified, divisibility_remainder, certificate] 欄序回答。

查看答案與解釋(6, 2, 是, 0, complete_group_and_prime_divisibility_hypotheses_hold)

Wave6第六層核對=(6, 2, 是, 0, complete_group_and_prime_divisibility_hypotheses_hold)；依完整明示資料獨立重算；order-p witness必須同時驗g^p=e與所有1<=k<p皆有g^k!=e；完整有限枚舉只證指定model；composite divisor不保證是某元素的階。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261112-r01-cauchy-theorem-finite-groups-0001/)

有限群的Cauchy定理 · qf-mod43-cauchy-prime-divisor-qualification · candidate





## 2. 有限群的Cauchy定理

完整有限群、prime divisor與exact element-order證書。操作=cauchy-prime-divisor-qualification；資料={"group_table":[[0,1,2,3,4,5,6,7],[1,2,3,4,5,6,7,0],[2,3,4,5,6,7,0,1],[3,4,5,6,7,0,1,2],[4,5,6,7,0,1,2,3],[5,6,7,0,1,2,3,4],[6,7,0,1,2,3,4,5],[7,0,1,2,3,4,5,6]],"identity":0,"prime":2}。請依 [group_order, prime, qualified, divisibility_remainder, certificate] 欄序回答。

查看答案與解釋(8, 2, 是, 0, complete_group_and_prime_divisibility_hypotheses_hold)

Wave6第六層核對=(8, 2, 是, 0, complete_group_and_prime_divisibility_hypotheses_hold)；依完整明示資料獨立重算；order-p witness必須同時驗g^p=e與所有1<=k<p皆有g^k!=e；完整有限枚舉只證指定model；composite divisor不保證是某元素的階。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261112-r01-cauchy-theorem-finite-groups-0002/)

有限群的Cauchy定理 · qf-mod43-cauchy-prime-divisor-qualification · candidate





## 3. 有限群的Cauchy定理

完整有限群、prime divisor與exact element-order證書。操作=cauchy-prime-divisor-qualification；資料={"group_table":[[0,1,2,3,4,5,6,7,8,9],[1,2,3,4,5,6,7,8,9,0],[2,3,4,5,6,7,8,9,0,1],[3,4,5,6,7,8,9,0,1,2],[4,5,6,7,8,9,0,1,2,3],[5,6,7,8,9,0,1,2,3,4],[6,7,8,9,0,1,2,3,4,5],[7,8,9,0,1,2,3,4,5,6],[8,9,0,1,2,3,4,5,6,7],[9,0,1,2,3,4,5,6,7,8]],"identity":0,"prime":2}。請依 [group_order, prime, qualified, divisibility_remainder, certificate] 欄序回答。

查看答案與解釋(10, 2, 是, 0, complete_group_and_prime_divisibility_hypotheses_hold)

Wave6第六層核對=(10, 2, 是, 0, complete_group_and_prime_divisibility_hypotheses_hold)；依完整明示資料獨立重算；order-p witness必須同時驗g^p=e與所有1<=k<p皆有g^k!=e；完整有限枚舉只證指定model；composite divisor不保證是某元素的階。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261112-r01-cauchy-theorem-finite-groups-0003/)

有限群的Cauchy定理 · qf-mod43-cauchy-prime-divisor-qualification · candidate





## 4. 有限群的Cauchy定理

完整有限群、prime divisor與exact element-order證書。操作=cauchy-prime-divisor-qualification；資料={"group_table":[[0,1,2,3,4,5,6,7,8,9,10,11],[1,2,3,4,5,6,7,8,9,10,11,0],[2,3,4,5,6,7,8,9,10,11,0,1],[3,4,5,6,7,8,9,10,11,0,1,2],[4,5,6,7,8,9,10,11,0,1,2,3],[5,6,7,8,9,10,11,0,1,2,3,4],[6,7,8,9,10,11,0,1,2,3,4,5],[7,8,9,10,11,0,1,2,3,4,5,6],[8,9,10,11,0,1,2,3,4,5,6,7],[9,10,11,0,1,2,3,4,5,6,7,8],[10,11,0,1,2,3,4,5,6,7,8,9],[11,0,1,2,3,4,5,6,7,8,9,10]],"identity":0,"prime":2}。請依 [group_order, prime, qualified, divisibility_remainder, certificate] 欄序回答。

查看答案與解釋(12, 2, 是, 0, complete_group_and_prime_divisibility_hypotheses_hold)

Wave6第六層核對=(12, 2, 是, 0, complete_group_and_prime_divisibility_hypotheses_hold)；依完整明示資料獨立重算；order-p witness必須同時驗g^p=e與所有1<=k<p皆有g^k!=e；完整有限枚舉只證指定model；composite divisor不保證是某元素的階。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261112-r01-cauchy-theorem-finite-groups-0004/)

有限群的Cauchy定理 · qf-mod43-cauchy-prime-divisor-qualification · candidate





## 5. 有限群的Cauchy定理

完整有限群、prime divisor與exact element-order證書。操作=cauchy-prime-divisor-qualification；資料={"group_table":[[0,1,2,3,4,5,6,7,8,9,10,11,12,13],[1,2,3,4,5,6,7,8,9,10,11,12,13,0],[2,3,4,5,6,7,8,9,10,11,12,13,0,1],[3,4,5,6,7,8,9,10,11,12,13,0,1,2],[4,5,6,7,8,9,10,11,12,13,0,1,2,3],[5,6,7,8,9,10,11,12,13,0,1,2,3,4],[6,7,8,9,10,11,12,13,0,1,2,3,4,5],[7,8,9,10,11,12,13,0,1,2,3,4,5,6],[8,9,10,11,12,13,0,1,2,3,4,5,6,7],[9,10,11,12,13,0,1,2,3,4,5,6,7,8],[10,11,12,13,0,1,2,3,4,5,6,7,8,9],[11,12,13,0,1,2,3,4,5,6,7,8,9,10],[12,13,0,1,2,3,4,5,6,7,8,9,10,11],[13,0,1,2,3,4,5,6,7,8,9,10,11,12]],"identity":0,"prime":2}。請依 [group_order, prime, qualified, divisibility_remainder, certificate] 欄序回答。

查看答案與解釋(14, 2, 是, 0, complete_group_and_prime_divisibility_hypotheses_hold)

Wave6第六層核對=(14, 2, 是, 0, complete_group_and_prime_divisibility_hypotheses_hold)；依完整明示資料獨立重算；order-p witness必須同時驗g^p=e與所有1<=k<p皆有g^k!=e；完整有限枚舉只證指定model；composite divisor不保證是某元素的階。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261112-r01-cauchy-theorem-finite-groups-0005/)

有限群的Cauchy定理 · qf-mod43-cauchy-prime-divisor-qualification · candidate





## 6. 有限群的Cauchy定理

完整有限群、prime divisor與exact element-order證書。操作=cauchy-prime-divisor-qualification；資料={"group_table":[[5,0,1,2,3,4],[0,1,2,3,4,5],[1,2,3,4,5,0],[2,3,4,5,0,1],[3,4,5,0,1,2],[4,5,0,1,2,3]],"identity":1,"prime":2}。請依 [group_order, prime, qualified, divisibility_remainder, certificate] 欄序回答。

查看答案與解釋(6, 2, 是, 0, complete_group_and_prime_divisibility_hypotheses_hold)

Wave6第六層核對=(6, 2, 是, 0, complete_group_and_prime_divisibility_hypotheses_hold)；依完整明示資料獨立重算；order-p witness必須同時驗g^p=e與所有1<=k<p皆有g^k!=e；完整有限枚舉只證指定model；composite divisor不保證是某元素的階。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261112-r01-cauchy-theorem-finite-groups-0006/)

有限群的Cauchy定理 · qf-mod43-cauchy-prime-divisor-qualification · candidate





## 7. 有限群的Cauchy定理

完整有限群、prime divisor與exact element-order證書。操作=cauchy-prime-divisor-qualification；資料={"group_table":[[7,0,1,2,3,4,5,6],[0,1,2,3,4,5,6,7],[1,2,3,4,5,6,7,0],[2,3,4,5,6,7,0,1],[3,4,5,6,7,0,1,2],[4,5,6,7,0,1,2,3],[5,6,7,0,1,2,3,4],[6,7,0,1,2,3,4,5]],"identity":1,"prime":2}。請依 [group_order, prime, qualified, divisibility_remainder, certificate] 欄序回答。

查看答案與解釋(8, 2, 是, 0, complete_group_and_prime_divisibility_hypotheses_hold)

Wave6第六層核對=(8, 2, 是, 0, complete_group_and_prime_divisibility_hypotheses_hold)；依完整明示資料獨立重算；order-p witness必須同時驗g^p=e與所有1<=k<p皆有g^k!=e；完整有限枚舉只證指定model；composite divisor不保證是某元素的階。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261112-r01-cauchy-theorem-finite-groups-0007/)

有限群的Cauchy定理 · qf-mod43-cauchy-prime-divisor-qualification · candidate





## 8. 有限群的Cauchy定理

完整有限群、prime divisor與exact element-order證書。操作=cauchy-prime-divisor-qualification；資料={"group_table":[[9,0,1,2,3,4,5,6,7,8],[0,1,2,3,4,5,6,7,8,9],[1,2,3,4,5,6,7,8,9,0],[2,3,4,5,6,7,8,9,0,1],[3,4,5,6,7,8,9,0,1,2],[4,5,6,7,8,9,0,1,2,3],[5,6,7,8,9,0,1,2,3,4],[6,7,8,9,0,1,2,3,4,5],[7,8,9,0,1,2,3,4,5,6],[8,9,0,1,2,3,4,5,6,7]],"identity":1,"prime":2}。請依 [group_order, prime, qualified, divisibility_remainder, certificate] 欄序回答。

查看答案與解釋(10, 2, 是, 0, complete_group_and_prime_divisibility_hypotheses_hold)

Wave6第六層核對=(10, 2, 是, 0, complete_group_and_prime_divisibility_hypotheses_hold)；依完整明示資料獨立重算；order-p witness必須同時驗g^p=e與所有1<=k<p皆有g^k!=e；完整有限枚舉只證指定model；composite divisor不保證是某元素的階。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261112-r01-cauchy-theorem-finite-groups-0008/)

有限群的Cauchy定理 · qf-mod43-cauchy-prime-divisor-qualification · candidate





## 9. 有限群的Cauchy定理

完整有限群、prime divisor與exact element-order證書。操作=cauchy-prime-divisor-qualification；資料={"group_table":[[11,0,1,2,3,4,5,6,7,8,9,10],[0,1,2,3,4,5,6,7,8,9,10,11],[1,2,3,4,5,6,7,8,9,10,11,0],[2,3,4,5,6,7,8,9,10,11,0,1],[3,4,5,6,7,8,9,10,11,0,1,2],[4,5,6,7,8,9,10,11,0,1,2,3],[5,6,7,8,9,10,11,0,1,2,3,4],[6,7,8,9,10,11,0,1,2,3,4,5],[7,8,9,10,11,0,1,2,3,4,5,6],[8,9,10,11,0,1,2,3,4,5,6,7],[9,10,11,0,1,2,3,4,5,6,7,8],[10,11,0,1,2,3,4,5,6,7,8,9]],"identity":1,"prime":2}。請依 [group_order, prime, qualified, divisibility_remainder, certificate] 欄序回答。

查看答案與解釋(12, 2, 是, 0, complete_group_and_prime_divisibility_hypotheses_hold)

Wave6第六層核對=(12, 2, 是, 0, complete_group_and_prime_divisibility_hypotheses_hold)；依完整明示資料獨立重算；order-p witness必須同時驗g^p=e與所有1<=k<p皆有g^k!=e；完整有限枚舉只證指定model；composite divisor不保證是某元素的階。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261112-r01-cauchy-theorem-finite-groups-0009/)

有限群的Cauchy定理 · qf-mod43-cauchy-prime-divisor-qualification · candidate





## 10. 有限群的Cauchy定理

完整有限群、prime divisor與exact element-order證書。操作=cauchy-prime-divisor-qualification；資料={"group_table":[[13,0,1,2,3,4,5,6,7,8,9,10,11,12],[0,1,2,3,4,5,6,7,8,9,10,11,12,13],[1,2,3,4,5,6,7,8,9,10,11,12,13,0],[2,3,4,5,6,7,8,9,10,11,12,13,0,1],[3,4,5,6,7,8,9,10,11,12,13,0,1,2],[4,5,6,7,8,9,10,11,12,13,0,1,2,3],[5,6,7,8,9,10,11,12,13,0,1,2,3,4],[6,7,8,9,10,11,12,13,0,1,2,3,4,5],[7,8,9,10,11,12,13,0,1,2,3,4,5,6],[8,9,10,11,12,13,0,1,2,3,4,5,6,7],[9,10,11,12,13,0,1,2,3,4,5,6,7,8],[10,11,12,13,0,1,2,3,4,5,6,7,8,9],[11,12,13,0,1,2,3,4,5,6,7,8,9,10],[12,13,0,1,2,3,4,5,6,7,8,9,10,11]],"identity":1,"prime":2}。請依 [group_order, prime, qualified, divisibility_remainder, certificate] 欄序回答。

查看答案與解釋(14, 2, 是, 0, complete_group_and_prime_divisibility_hypotheses_hold)

Wave6第六層核對=(14, 2, 是, 0, complete_group_and_prime_divisibility_hypotheses_hold)；依完整明示資料獨立重算；order-p witness必須同時驗g^p=e與所有1<=k<p皆有g^k!=e；完整有限枚舉只證指定model；composite divisor不保證是某元素的階。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261112-r01-cauchy-theorem-finite-groups-0010/)

有限群的Cauchy定理 · qf-mod43-cauchy-prime-divisor-qualification · candidate





## 11. 有限群的Cauchy定理

完整有限群、prime divisor與exact element-order證書。操作=cauchy-prime-divisor-qualification；資料={"group_table":[[4,5,0,1,2,3],[5,0,1,2,3,4],[0,1,2,3,4,5],[1,2,3,4,5,0],[2,3,4,5,0,1],[3,4,5,0,1,2]],"identity":2,"prime":2}。請依 [group_order, prime, qualified, divisibility_remainder, certificate] 欄序回答。

查看答案與解釋(6, 2, 是, 0, complete_group_and_prime_divisibility_hypotheses_hold)

Wave6第六層核對=(6, 2, 是, 0, complete_group_and_prime_divisibility_hypotheses_hold)；依完整明示資料獨立重算；order-p witness必須同時驗g^p=e與所有1<=k<p皆有g^k!=e；完整有限枚舉只證指定model；composite divisor不保證是某元素的階。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261112-r01-cauchy-theorem-finite-groups-0011/)

有限群的Cauchy定理 · qf-mod43-cauchy-prime-divisor-qualification · candidate





## 12. 有限群的Cauchy定理

完整有限群、prime divisor與exact element-order證書。操作=cauchy-prime-divisor-qualification；資料={"group_table":[[6,7,0,1,2,3,4,5],[7,0,1,2,3,4,5,6],[0,1,2,3,4,5,6,7],[1,2,3,4,5,6,7,0],[2,3,4,5,6,7,0,1],[3,4,5,6,7,0,1,2],[4,5,6,7,0,1,2,3],[5,6,7,0,1,2,3,4]],"identity":2,"prime":2}。請依 [group_order, prime, qualified, divisibility_remainder, certificate] 欄序回答。

查看答案與解釋(8, 2, 是, 0, complete_group_and_prime_divisibility_hypotheses_hold)

Wave6第六層核對=(8, 2, 是, 0, complete_group_and_prime_divisibility_hypotheses_hold)；依完整明示資料獨立重算；order-p witness必須同時驗g^p=e與所有1<=k<p皆有g^k!=e；完整有限枚舉只證指定model；composite divisor不保證是某元素的階。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261112-r01-cauchy-theorem-finite-groups-0012/)

有限群的Cauchy定理 · qf-mod43-cauchy-prime-divisor-qualification · candidate





## 13. 有限群的Cauchy定理

完整有限群、prime divisor與exact element-order證書。操作=cauchy-prime-divisor-qualification；資料={"group_table":[[8,9,0,1,2,3,4,5,6,7],[9,0,1,2,3,4,5,6,7,8],[0,1,2,3,4,5,6,7,8,9],[1,2,3,4,5,6,7,8,9,0],[2,3,4,5,6,7,8,9,0,1],[3,4,5,6,7,8,9,0,1,2],[4,5,6,7,8,9,0,1,2,3],[5,6,7,8,9,0,1,2,3,4],[6,7,8,9,0,1,2,3,4,5],[7,8,9,0,1,2,3,4,5,6]],"identity":2,"prime":2}。請依 [group_order, prime, qualified, divisibility_remainder, certificate] 欄序回答。

查看答案與解釋(10, 2, 是, 0, complete_group_and_prime_divisibility_hypotheses_hold)

Wave6第六層核對=(10, 2, 是, 0, complete_group_and_prime_divisibility_hypotheses_hold)；依完整明示資料獨立重算；order-p witness必須同時驗g^p=e與所有1<=k<p皆有g^k!=e；完整有限枚舉只證指定model；composite divisor不保證是某元素的階。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261112-r01-cauchy-theorem-finite-groups-0013/)

有限群的Cauchy定理 · qf-mod43-cauchy-prime-divisor-qualification · candidate





## 14. 有限群的Cauchy定理

完整有限群、prime divisor與exact element-order證書。操作=cauchy-prime-divisor-qualification；資料={"group_table":[[10,11,0,1,2,3,4,5,6,7,8,9],[11,0,1,2,3,4,5,6,7,8,9,10],[0,1,2,3,4,5,6,7,8,9,10,11],[1,2,3,4,5,6,7,8,9,10,11,0],[2,3,4,5,6,7,8,9,10,11,0,1],[3,4,5,6,7,8,9,10,11,0,1,2],[4,5,6,7,8,9,10,11,0,1,2,3],[5,6,7,8,9,10,11,0,1,2,3,4],[6,7,8,9,10,11,0,1,2,3,4,5],[7,8,9,10,11,0,1,2,3,4,5,6],[8,9,10,11,0,1,2,3,4,5,6,7],[9,10,11,0,1,2,3,4,5,6,7,8]],"identity":2,"prime":2}。請依 [group_order, prime, qualified, divisibility_remainder, certificate] 欄序回答。

查看答案與解釋(12, 2, 是, 0, complete_group_and_prime_divisibility_hypotheses_hold)

Wave6第六層核對=(12, 2, 是, 0, complete_group_and_prime_divisibility_hypotheses_hold)；依完整明示資料獨立重算；order-p witness必須同時驗g^p=e與所有1<=k<p皆有g^k!=e；完整有限枚舉只證指定model；composite divisor不保證是某元素的階。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261112-r01-cauchy-theorem-finite-groups-0014/)

有限群的Cauchy定理 · qf-mod43-cauchy-prime-divisor-qualification · candidate





## 15. 有限群的Cauchy定理

完整有限群、prime divisor與exact element-order證書。操作=cauchy-prime-divisor-qualification；資料={"group_table":[[12,13,0,1,2,3,4,5,6,7,8,9,10,11],[13,0,1,2,3,4,5,6,7,8,9,10,11,12],[0,1,2,3,4,5,6,7,8,9,10,11,12,13],[1,2,3,4,5,6,7,8,9,10,11,12,13,0],[2,3,4,5,6,7,8,9,10,11,12,13,0,1],[3,4,5,6,7,8,9,10,11,12,13,0,1,2],[4,5,6,7,8,9,10,11,12,13,0,1,2,3],[5,6,7,8,9,10,11,12,13,0,1,2,3,4],[6,7,8,9,10,11,12,13,0,1,2,3,4,5],[7,8,9,10,11,12,13,0,1,2,3,4,5,6],[8,9,10,11,12,13,0,1,2,3,4,5,6,7],[9,10,11,12,13,0,1,2,3,4,5,6,7,8],[10,11,12,13,0,1,2,3,4,5,6,7,8,9],[11,12,13,0,1,2,3,4,5,6,7,8,9,10]],"identity":2,"prime":2}。請依 [group_order, prime, qualified, divisibility_remainder, certificate] 欄序回答。

查看答案與解釋(14, 2, 是, 0, complete_group_and_prime_divisibility_hypotheses_hold)

Wave6第六層核對=(14, 2, 是, 0, complete_group_and_prime_divisibility_hypotheses_hold)；依完整明示資料獨立重算；order-p witness必須同時驗g^p=e與所有1<=k<p皆有g^k!=e；完整有限枚舉只證指定model；composite divisor不保證是某元素的階。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261112-r01-cauchy-theorem-finite-groups-0015/)

有限群的Cauchy定理 · qf-mod43-cauchy-prime-divisor-qualification · candidate





## 16. 有限群的Cauchy定理

完整有限群、prime divisor與exact element-order證書。操作=cauchy-prime-divisor-qualification；資料={"group_table":[[3,4,5,0,1,2],[4,5,0,1,2,3],[5,0,1,2,3,4],[0,1,2,3,4,5],[1,2,3,4,5,0],[2,3,4,5,0,1]],"identity":3,"prime":2}。請依 [group_order, prime, qualified, divisibility_remainder, certificate] 欄序回答。

查看答案與解釋(6, 2, 是, 0, complete_group_and_prime_divisibility_hypotheses_hold)

Wave6第六層核對=(6, 2, 是, 0, complete_group_and_prime_divisibility_hypotheses_hold)；依完整明示資料獨立重算；order-p witness必須同時驗g^p=e與所有1<=k<p皆有g^k!=e；完整有限枚舉只證指定model；composite divisor不保證是某元素的階。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261112-r01-cauchy-theorem-finite-groups-0016/)

有限群的Cauchy定理 · qf-mod43-cauchy-prime-divisor-qualification · candidate





## 17. 有限群的Cauchy定理

完整有限群、prime divisor與exact element-order證書。操作=cauchy-prime-divisor-qualification；資料={"group_table":[[5,6,7,0,1,2,3,4],[6,7,0,1,2,3,4,5],[7,0,1,2,3,4,5,6],[0,1,2,3,4,5,6,7],[1,2,3,4,5,6,7,0],[2,3,4,5,6,7,0,1],[3,4,5,6,7,0,1,2],[4,5,6,7,0,1,2,3]],"identity":3,"prime":2}。請依 [group_order, prime, qualified, divisibility_remainder, certificate] 欄序回答。

查看答案與解釋(8, 2, 是, 0, complete_group_and_prime_divisibility_hypotheses_hold)

Wave6第六層核對=(8, 2, 是, 0, complete_group_and_prime_divisibility_hypotheses_hold)；依完整明示資料獨立重算；order-p witness必須同時驗g^p=e與所有1<=k<p皆有g^k!=e；完整有限枚舉只證指定model；composite divisor不保證是某元素的階。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261112-r01-cauchy-theorem-finite-groups-0017/)

有限群的Cauchy定理 · qf-mod43-cauchy-prime-divisor-qualification · candidate





## 18. 有限群的Cauchy定理

完整有限群、prime divisor與exact element-order證書。操作=cauchy-prime-divisor-qualification；資料={"group_table":[[7,8,9,0,1,2,3,4,5,6],[8,9,0,1,2,3,4,5,6,7],[9,0,1,2,3,4,5,6,7,8],[0,1,2,3,4,5,6,7,8,9],[1,2,3,4,5,6,7,8,9,0],[2,3,4,5,6,7,8,9,0,1],[3,4,5,6,7,8,9,0,1,2],[4,5,6,7,8,9,0,1,2,3],[5,6,7,8,9,0,1,2,3,4],[6,7,8,9,0,1,2,3,4,5]],"identity":3,"prime":2}。請依 [group_order, prime, qualified, divisibility_remainder, certificate] 欄序回答。

查看答案與解釋(10, 2, 是, 0, complete_group_and_prime_divisibility_hypotheses_hold)

Wave6第六層核對=(10, 2, 是, 0, complete_group_and_prime_divisibility_hypotheses_hold)；依完整明示資料獨立重算；order-p witness必須同時驗g^p=e與所有1<=k<p皆有g^k!=e；完整有限枚舉只證指定model；composite divisor不保證是某元素的階。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261112-r01-cauchy-theorem-finite-groups-0018/)

有限群的Cauchy定理 · qf-mod43-cauchy-prime-divisor-qualification · candidate





## 19. 有限群的Cauchy定理

完整有限群、prime divisor與exact element-order證書。操作=cauchy-prime-divisor-qualification；資料={"group_table":[[9,10,11,0,1,2,3,4,5,6,7,8],[10,11,0,1,2,3,4,5,6,7,8,9],[11,0,1,2,3,4,5,6,7,8,9,10],[0,1,2,3,4,5,6,7,8,9,10,11],[1,2,3,4,5,6,7,8,9,10,11,0],[2,3,4,5,6,7,8,9,10,11,0,1],[3,4,5,6,7,8,9,10,11,0,1,2],[4,5,6,7,8,9,10,11,0,1,2,3],[5,6,7,8,9,10,11,0,1,2,3,4],[6,7,8,9,10,11,0,1,2,3,4,5],[7,8,9,10,11,0,1,2,3,4,5,6],[8,9,10,11,0,1,2,3,4,5,6,7]],"identity":3,"prime":2}。請依 [group_order, prime, qualified, divisibility_remainder, certificate] 欄序回答。

查看答案與解釋(12, 2, 是, 0, complete_group_and_prime_divisibility_hypotheses_hold)

Wave6第六層核對=(12, 2, 是, 0, complete_group_and_prime_divisibility_hypotheses_hold)；依完整明示資料獨立重算；order-p witness必須同時驗g^p=e與所有1<=k<p皆有g^k!=e；完整有限枚舉只證指定model；composite divisor不保證是某元素的階。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261112-r01-cauchy-theorem-finite-groups-0019/)

有限群的Cauchy定理 · qf-mod43-cauchy-prime-divisor-qualification · candidate





## 20. 有限群的Cauchy定理

完整有限群、prime divisor與exact element-order證書。操作=cauchy-prime-divisor-qualification；資料={"group_table":[[11,12,13,0,1,2,3,4,5,6,7,8,9,10],[12,13,0,1,2,3,4,5,6,7,8,9,10,11],[13,0,1,2,3,4,5,6,7,8,9,10,11,12],[0,1,2,3,4,5,6,7,8,9,10,11,12,13],[1,2,3,4,5,6,7,8,9,10,11,12,13,0],[2,3,4,5,6,7,8,9,10,11,12,13,0,1],[3,4,5,6,7,8,9,10,11,12,13,0,1,2],[4,5,6,7,8,9,10,11,12,13,0,1,2,3],[5,6,7,8,9,10,11,12,13,0,1,2,3,4],[6,7,8,9,10,11,12,13,0,1,2,3,4,5],[7,8,9,10,11,12,13,0,1,2,3,4,5,6],[8,9,10,11,12,13,0,1,2,3,4,5,6,7],[9,10,11,12,13,0,1,2,3,4,5,6,7,8],[10,11,12,13,0,1,2,3,4,5,6,7,8,9]],"identity":3,"prime":2}。請依 [group_order, prime, qualified, divisibility_remainder, certificate] 欄序回答。

查看答案與解釋(14, 2, 是, 0, complete_group_and_prime_divisibility_hypotheses_hold)

Wave6第六層核對=(14, 2, 是, 0, complete_group_and_prime_divisibility_hypotheses_hold)；依完整明示資料獨立重算；order-p witness必須同時驗g^p=e與所有1<=k<p皆有g^k!=e；完整有限枚舉只證指定model；composite divisor不保證是某元素的階。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261112-r01-cauchy-theorem-finite-groups-0020/)

有限群的Cauchy定理 · qf-mod43-cauchy-prime-divisor-qualification · candidate





## 21. 有限群的Cauchy定理

完整有限群、prime divisor與exact element-order證書。操作=cauchy-prime-divisor-qualification；資料={"group_table":[[2,3,4,5,0,1],[3,4,5,0,1,2],[4,5,0,1,2,3],[5,0,1,2,3,4],[0,1,2,3,4,5],[1,2,3,4,5,0]],"identity":4,"prime":2}。請依 [group_order, prime, qualified, divisibility_remainder, certificate] 欄序回答。

查看答案與解釋(6, 2, 是, 0, complete_group_and_prime_divisibility_hypotheses_hold)

Wave6第六層核對=(6, 2, 是, 0, complete_group_and_prime_divisibility_hypotheses_hold)；依完整明示資料獨立重算；order-p witness必須同時驗g^p=e與所有1<=k<p皆有g^k!=e；完整有限枚舉只證指定model；composite divisor不保證是某元素的階。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261112-r01-cauchy-theorem-finite-groups-0021/)

有限群的Cauchy定理 · qf-mod43-cauchy-prime-divisor-qualification · candidate





## 22. 有限群的Cauchy定理

完整有限群、prime divisor與exact element-order證書。操作=cauchy-prime-divisor-qualification；資料={"group_table":[[4,5,6,7,0,1,2,3],[5,6,7,0,1,2,3,4],[6,7,0,1,2,3,4,5],[7,0,1,2,3,4,5,6],[0,1,2,3,4,5,6,7],[1,2,3,4,5,6,7,0],[2,3,4,5,6,7,0,1],[3,4,5,6,7,0,1,2]],"identity":4,"prime":2}。請依 [group_order, prime, qualified, divisibility_remainder, certificate] 欄序回答。

查看答案與解釋(8, 2, 是, 0, complete_group_and_prime_divisibility_hypotheses_hold)

Wave6第六層核對=(8, 2, 是, 0, complete_group_and_prime_divisibility_hypotheses_hold)；依完整明示資料獨立重算；order-p witness必須同時驗g^p=e與所有1<=k<p皆有g^k!=e；完整有限枚舉只證指定model；composite divisor不保證是某元素的階。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261112-r01-cauchy-theorem-finite-groups-0022/)

有限群的Cauchy定理 · qf-mod43-cauchy-prime-divisor-qualification · candidate





## 23. 有限群的Cauchy定理

完整有限群、prime divisor與exact element-order證書。操作=cauchy-prime-divisor-qualification；資料={"group_table":[[6,7,8,9,0,1,2,3,4,5],[7,8,9,0,1,2,3,4,5,6],[8,9,0,1,2,3,4,5,6,7],[9,0,1,2,3,4,5,6,7,8],[0,1,2,3,4,5,6,7,8,9],[1,2,3,4,5,6,7,8,9,0],[2,3,4,5,6,7,8,9,0,1],[3,4,5,6,7,8,9,0,1,2],[4,5,6,7,8,9,0,1,2,3],[5,6,7,8,9,0,1,2,3,4]],"identity":4,"prime":2}。請依 [group_order, prime, qualified, divisibility_remainder, certificate] 欄序回答。

查看答案與解釋(10, 2, 是, 0, complete_group_and_prime_divisibility_hypotheses_hold)

Wave6第六層核對=(10, 2, 是, 0, complete_group_and_prime_divisibility_hypotheses_hold)；依完整明示資料獨立重算；order-p witness必須同時驗g^p=e與所有1<=k<p皆有g^k!=e；完整有限枚舉只證指定model；composite divisor不保證是某元素的階。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261112-r01-cauchy-theorem-finite-groups-0023/)

有限群的Cauchy定理 · qf-mod43-cauchy-prime-divisor-qualification · candidate





## 24. 有限群的Cauchy定理

完整有限群、prime divisor與exact element-order證書。操作=cauchy-prime-divisor-qualification；資料={"group_table":[[8,9,10,11,0,1,2,3,4,5,6,7],[9,10,11,0,1,2,3,4,5,6,7,8],[10,11,0,1,2,3,4,5,6,7,8,9],[11,0,1,2,3,4,5,6,7,8,9,10],[0,1,2,3,4,5,6,7,8,9,10,11],[1,2,3,4,5,6,7,8,9,10,11,0],[2,3,4,5,6,7,8,9,10,11,0,1],[3,4,5,6,7,8,9,10,11,0,1,2],[4,5,6,7,8,9,10,11,0,1,2,3],[5,6,7,8,9,10,11,0,1,2,3,4],[6,7,8,9,10,11,0,1,2,3,4,5],[7,8,9,10,11,0,1,2,3,4,5,6]],"identity":4,"prime":2}。請依 [group_order, prime, qualified, divisibility_remainder, certificate] 欄序回答。

查看答案與解釋(12, 2, 是, 0, complete_group_and_prime_divisibility_hypotheses_hold)

Wave6第六層核對=(12, 2, 是, 0, complete_group_and_prime_divisibility_hypotheses_hold)；依完整明示資料獨立重算；order-p witness必須同時驗g^p=e與所有1<=k<p皆有g^k!=e；完整有限枚舉只證指定model；composite divisor不保證是某元素的階。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261112-r01-cauchy-theorem-finite-groups-0024/)

有限群的Cauchy定理 · qf-mod43-cauchy-prime-divisor-qualification · candidate





## 25. 有限群的Cauchy定理

完整有限群、prime divisor與exact element-order證書。操作=cauchy-prime-divisor-qualification；資料={"group_table":[[10,11,12,13,0,1,2,3,4,5,6,7,8,9],[11,12,13,0,1,2,3,4,5,6,7,8,9,10],[12,13,0,1,2,3,4,5,6,7,8,9,10,11],[13,0,1,2,3,4,5,6,7,8,9,10,11,12],[0,1,2,3,4,5,6,7,8,9,10,11,12,13],[1,2,3,4,5,6,7,8,9,10,11,12,13,0],[2,3,4,5,6,7,8,9,10,11,12,13,0,1],[3,4,5,6,7,8,9,10,11,12,13,0,1,2],[4,5,6,7,8,9,10,11,12,13,0,1,2,3],[5,6,7,8,9,10,11,12,13,0,1,2,3,4],[6,7,8,9,10,11,12,13,0,1,2,3,4,5],[7,8,9,10,11,12,13,0,1,2,3,4,5,6],[8,9,10,11,12,13,0,1,2,3,4,5,6,7],[9,10,11,12,13,0,1,2,3,4,5,6,7,8]],"identity":4,"prime":2}。請依 [group_order, prime, qualified, divisibility_remainder, certificate] 欄序回答。

查看答案與解釋(14, 2, 是, 0, complete_group_and_prime_divisibility_hypotheses_hold)

Wave6第六層核對=(14, 2, 是, 0, complete_group_and_prime_divisibility_hypotheses_hold)；依完整明示資料獨立重算；order-p witness必須同時驗g^p=e與所有1<=k<p皆有g^k!=e；完整有限枚舉只證指定model；composite divisor不保證是某元素的階。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261112-r01-cauchy-theorem-finite-groups-0025/)

有限群的Cauchy定理 · qf-mod43-cauchy-prime-divisor-qualification · candidate





## 26. 有限群的Cauchy定理

完整有限群、prime divisor與exact element-order證書。操作=cauchy-element-order-table；資料={"group_table":[[0,1,2,3,4,5],[1,2,3,4,5,0],[2,3,4,5,0,1],[3,4,5,0,1,2],[4,5,0,1,2,3],[5,0,1,2,3,4]],"identity":0}。請依 [group_order, element_order_rows, all_orders_divide_group_order, certificate] 欄序回答。

查看答案與解釋(6, [[0, 1], [1, 6], [2, 3], [3, 2], [4, 3], [5, 6]], 是, complete_element_order_table_for_declared_finite_group)

Wave6第六層核對=(6, [[0, 1], [1, 6], [2, 3], [3, 2], [4, 3], [5, 6]], 是, complete_element_order_table_for_declared_finite_group)；依完整明示資料獨立重算；order-p witness必須同時驗g^p=e與所有1<=k<p皆有g^k!=e；完整有限枚舉只證指定model；composite divisor不保證是某元素的階。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261112-r01-cauchy-theorem-finite-groups-0026/)

有限群的Cauchy定理 · qf-mod43-cauchy-element-order-table · candidate





## 27. 有限群的Cauchy定理

完整有限群、prime divisor與exact element-order證書。操作=cauchy-element-order-table；資料={"group_table":[[0,1,2,3,4,5,6,7],[1,2,3,4,5,6,7,0],[2,3,4,5,6,7,0,1],[3,4,5,6,7,0,1,2],[4,5,6,7,0,1,2,3],[5,6,7,0,1,2,3,4],[6,7,0,1,2,3,4,5],[7,0,1,2,3,4,5,6]],"identity":0}。請依 [group_order, element_order_rows, all_orders_divide_group_order, certificate] 欄序回答。

查看答案與解釋(8, [[0, 1], [1, 8], [2, 4], [3, 8], [4, 2], [5, 8], [6, 4], [7, 8]], 是, complete_element_order_table_for_declared_finite_group)

Wave6第六層核對=(8, [[0, 1], [1, 8], [2, 4], [3, 8], [4, 2], [5, 8], [6, 4], [7, 8]], 是, complete_element_order_table_for_declared_finite_group)；依完整明示資料獨立重算；order-p witness必須同時驗g^p=e與所有1<=k<p皆有g^k!=e；完整有限枚舉只證指定model；composite divisor不保證是某元素的階。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261112-r01-cauchy-theorem-finite-groups-0027/)

有限群的Cauchy定理 · qf-mod43-cauchy-element-order-table · candidate





## 28. 有限群的Cauchy定理

完整有限群、prime divisor與exact element-order證書。操作=cauchy-element-order-table；資料={"group_table":[[0,1,2,3,4,5,6,7,8,9],[1,2,3,4,5,6,7,8,9,0],[2,3,4,5,6,7,8,9,0,1],[3,4,5,6,7,8,9,0,1,2],[4,5,6,7,8,9,0,1,2,3],[5,6,7,8,9,0,1,2,3,4],[6,7,8,9,0,1,2,3,4,5],[7,8,9,0,1,2,3,4,5,6],[8,9,0,1,2,3,4,5,6,7],[9,0,1,2,3,4,5,6,7,8]],"identity":0}。請依 [group_order, element_order_rows, all_orders_divide_group_order, certificate] 欄序回答。

查看答案與解釋(10, [[0, 1], [1, 10], [2, 5], [3, 10], [4, 5], [5, 2], [6, 5], [7, 10], [8, 5], [9, 10]], 是, complete_element_order_table_for_declared_finite_group)

Wave6第六層核對=(10, [[0, 1], [1, 10], [2, 5], [3, 10], [4, 5], [5, 2], [6, 5], [7, 10], [8, 5], [9, 10]], 是, complete_element_order_table_for_declared_finite_group)；依完整明示資料獨立重算；order-p witness必須同時驗g^p=e與所有1<=k<p皆有g^k!=e；完整有限枚舉只證指定model；composite divisor不保證是某元素的階。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261112-r01-cauchy-theorem-finite-groups-0028/)

有限群的Cauchy定理 · qf-mod43-cauchy-element-order-table · candidate





## 29. 有限群的Cauchy定理

完整有限群、prime divisor與exact element-order證書。操作=cauchy-element-order-table；資料={"group_table":[[0,1,2,3,4,5,6,7,8,9,10,11],[1,2,3,4,5,6,7,8,9,10,11,0],[2,3,4,5,6,7,8,9,10,11,0,1],[3,4,5,6,7,8,9,10,11,0,1,2],[4,5,6,7,8,9,10,11,0,1,2,3],[5,6,7,8,9,10,11,0,1,2,3,4],[6,7,8,9,10,11,0,1,2,3,4,5],[7,8,9,10,11,0,1,2,3,4,5,6],[8,9,10,11,0,1,2,3,4,5,6,7],[9,10,11,0,1,2,3,4,5,6,7,8],[10,11,0,1,2,3,4,5,6,7,8,9],[11,0,1,2,3,4,5,6,7,8,9,10]],"identity":0}。請依 [group_order, element_order_rows, all_orders_divide_group_order, certificate] 欄序回答。

查看答案與解釋(12, [[0, 1], [1, 12], [2, 6], [3, 4], [4, 3], [5, 12], [6, 2], [7, 12], [8, 3], [9, 4], [10, 6], [11, 12]], 是, complete_element_order_table_for_declared_finite_group)

Wave6第六層核對=(12, [[0, 1], [1, 12], [2, 6], [3, 4], [4, 3], [5, 12], [6, 2], [7, 12], [8, 3], [9, 4], [10, 6], [11, 12]], 是, complete_element_order_table_for_declared_finite_group)；依完整明示資料獨立重算；order-p witness必須同時驗g^p=e與所有1<=k<p皆有g^k!=e；完整有限枚舉只證指定model；composite divisor不保證是某元素的階。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261112-r01-cauchy-theorem-finite-groups-0029/)

有限群的Cauchy定理 · qf-mod43-cauchy-element-order-table · candidate





## 30. 有限群的Cauchy定理

完整有限群、prime divisor與exact element-order證書。操作=cauchy-element-order-table；資料={"group_table":[[0,1,2,3,4,5,6,7,8,9,10,11,12,13],[1,2,3,4,5,6,7,8,9,10,11,12,13,0],[2,3,4,5,6,7,8,9,10,11,12,13,0,1],[3,4,5,6,7,8,9,10,11,12,13,0,1,2],[4,5,6,7,8,9,10,11,12,13,0,1,2,3],[5,6,7,8,9,10,11,12,13,0,1,2,3,4],[6,7,8,9,10,11,12,13,0,1,2,3,4,5],[7,8,9,10,11,12,13,0,1,2,3,4,5,6],[8,9,10,11,12,13,0,1,2,3,4,5,6,7],[9,10,11,12,13,0,1,2,3,4,5,6,7,8],[10,11,12,13,0,1,2,3,4,5,6,7,8,9],[11,12,13,0,1,2,3,4,5,6,7,8,9,10],[12,13,0,1,2,3,4,5,6,7,8,9,10,11],[13,0,1,2,3,4,5,6,7,8,9,10,11,12]],"identity":0}。請依 [group_order, element_order_rows, all_orders_divide_group_order, certificate] 欄序回答。

查看答案與解釋(14, [[0, 1], [1, 14], [2, 7], [3, 14], [4, 7], [5, 14], [6, 7], [7, 2], [8, 7], [9, 14], [10, 7], [11, 14], [12, 7], [13, 14]], 是, complete_element_order_table_for_declared_finite_group)

Wave6第六層核對=(14, [[0, 1], [1, 14], [2, 7], [3, 14], [4, 7], [5, 14], [6, 7], [7, 2], [8, 7], [9, 14], [10, 7], [11, 14], [12, 7], [13, 14]], 是, complete_element_order_table_for_declared_finite_group)；依完整明示資料獨立重算；order-p witness必須同時驗g^p=e與所有1<=k<p皆有g^k!=e；完整有限枚舉只證指定model；composite divisor不保證是某元素的階。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261112-r01-cauchy-theorem-finite-groups-0030/)

有限群的Cauchy定理 · qf-mod43-cauchy-element-order-table · candidate





## 31. 有限群的Cauchy定理

完整有限群、prime divisor與exact element-order證書。操作=cauchy-element-order-table；資料={"group_table":[[5,0,1,2,3,4],[0,1,2,3,4,5],[1,2,3,4,5,0],[2,3,4,5,0,1],[3,4,5,0,1,2],[4,5,0,1,2,3]],"identity":1}。請依 [group_order, element_order_rows, all_orders_divide_group_order, certificate] 欄序回答。

查看答案與解釋(6, [[0, 6], [1, 1], [2, 6], [3, 3], [4, 2], [5, 3]], 是, complete_element_order_table_for_declared_finite_group)

Wave6第六層核對=(6, [[0, 6], [1, 1], [2, 6], [3, 3], [4, 2], [5, 3]], 是, complete_element_order_table_for_declared_finite_group)；依完整明示資料獨立重算；order-p witness必須同時驗g^p=e與所有1<=k<p皆有g^k!=e；完整有限枚舉只證指定model；composite divisor不保證是某元素的階。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261112-r01-cauchy-theorem-finite-groups-0031/)

有限群的Cauchy定理 · qf-mod43-cauchy-element-order-table · candidate





## 32. 有限群的Cauchy定理

完整有限群、prime divisor與exact element-order證書。操作=cauchy-element-order-table；資料={"group_table":[[7,0,1,2,3,4,5,6],[0,1,2,3,4,5,6,7],[1,2,3,4,5,6,7,0],[2,3,4,5,6,7,0,1],[3,4,5,6,7,0,1,2],[4,5,6,7,0,1,2,3],[5,6,7,0,1,2,3,4],[6,7,0,1,2,3,4,5]],"identity":1}。請依 [group_order, element_order_rows, all_orders_divide_group_order, certificate] 欄序回答。

查看答案與解釋(8, [[0, 8], [1, 1], [2, 8], [3, 4], [4, 8], [5, 2], [6, 8], [7, 4]], 是, complete_element_order_table_for_declared_finite_group)

Wave6第六層核對=(8, [[0, 8], [1, 1], [2, 8], [3, 4], [4, 8], [5, 2], [6, 8], [7, 4]], 是, complete_element_order_table_for_declared_finite_group)；依完整明示資料獨立重算；order-p witness必須同時驗g^p=e與所有1<=k<p皆有g^k!=e；完整有限枚舉只證指定model；composite divisor不保證是某元素的階。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261112-r01-cauchy-theorem-finite-groups-0032/)

有限群的Cauchy定理 · qf-mod43-cauchy-element-order-table · candidate





## 33. 有限群的Cauchy定理

完整有限群、prime divisor與exact element-order證書。操作=cauchy-element-order-table；資料={"group_table":[[9,0,1,2,3,4,5,6,7,8],[0,1,2,3,4,5,6,7,8,9],[1,2,3,4,5,6,7,8,9,0],[2,3,4,5,6,7,8,9,0,1],[3,4,5,6,7,8,9,0,1,2],[4,5,6,7,8,9,0,1,2,3],[5,6,7,8,9,0,1,2,3,4],[6,7,8,9,0,1,2,3,4,5],[7,8,9,0,1,2,3,4,5,6],[8,9,0,1,2,3,4,5,6,7]],"identity":1}。請依 [group_order, element_order_rows, all_orders_divide_group_order, certificate] 欄序回答。

查看答案與解釋(10, [[0, 10], [1, 1], [2, 10], [3, 5], [4, 10], [5, 5], [6, 2], [7, 5], [8, 10], [9, 5]], 是, complete_element_order_table_for_declared_finite_group)

Wave6第六層核對=(10, [[0, 10], [1, 1], [2, 10], [3, 5], [4, 10], [5, 5], [6, 2], [7, 5], [8, 10], [9, 5]], 是, complete_element_order_table_for_declared_finite_group)；依完整明示資料獨立重算；order-p witness必須同時驗g^p=e與所有1<=k<p皆有g^k!=e；完整有限枚舉只證指定model；composite divisor不保證是某元素的階。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261112-r01-cauchy-theorem-finite-groups-0033/)

有限群的Cauchy定理 · qf-mod43-cauchy-element-order-table · candidate





## 34. 有限群的Cauchy定理

完整有限群、prime divisor與exact element-order證書。操作=cauchy-element-order-table；資料={"group_table":[[11,0,1,2,3,4,5,6,7,8,9,10],[0,1,2,3,4,5,6,7,8,9,10,11],[1,2,3,4,5,6,7,8,9,10,11,0],[2,3,4,5,6,7,8,9,10,11,0,1],[3,4,5,6,7,8,9,10,11,0,1,2],[4,5,6,7,8,9,10,11,0,1,2,3],[5,6,7,8,9,10,11,0,1,2,3,4],[6,7,8,9,10,11,0,1,2,3,4,5],[7,8,9,10,11,0,1,2,3,4,5,6],[8,9,10,11,0,1,2,3,4,5,6,7],[9,10,11,0,1,2,3,4,5,6,7,8],[10,11,0,1,2,3,4,5,6,7,8,9]],"identity":1}。請依 [group_order, element_order_rows, all_orders_divide_group_order, certificate] 欄序回答。

查看答案與解釋(12, [[0, 12], [1, 1], [2, 12], [3, 6], [4, 4], [5, 3], [6, 12], [7, 2], [8, 12], [9, 3], [10, 4], [11, 6]], 是, complete_element_order_table_for_declared_finite_group)

Wave6第六層核對=(12, [[0, 12], [1, 1], [2, 12], [3, 6], [4, 4], [5, 3], [6, 12], [7, 2], [8, 12], [9, 3], [10, 4], [11, 6]], 是, complete_element_order_table_for_declared_finite_group)；依完整明示資料獨立重算；order-p witness必須同時驗g^p=e與所有1<=k<p皆有g^k!=e；完整有限枚舉只證指定model；composite divisor不保證是某元素的階。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261112-r01-cauchy-theorem-finite-groups-0034/)

有限群的Cauchy定理 · qf-mod43-cauchy-element-order-table · candidate





## 35. 有限群的Cauchy定理

完整有限群、prime divisor與exact element-order證書。操作=cauchy-element-order-table；資料={"group_table":[[13,0,1,2,3,4,5,6,7,8,9,10,11,12],[0,1,2,3,4,5,6,7,8,9,10,11,12,13],[1,2,3,4,5,6,7,8,9,10,11,12,13,0],[2,3,4,5,6,7,8,9,10,11,12,13,0,1],[3,4,5,6,7,8,9,10,11,12,13,0,1,2],[4,5,6,7,8,9,10,11,12,13,0,1,2,3],[5,6,7,8,9,10,11,12,13,0,1,2,3,4],[6,7,8,9,10,11,12,13,0,1,2,3,4,5],[7,8,9,10,11,12,13,0,1,2,3,4,5,6],[8,9,10,11,12,13,0,1,2,3,4,5,6,7],[9,10,11,12,13,0,1,2,3,4,5,6,7,8],[10,11,12,13,0,1,2,3,4,5,6,7,8,9],[11,12,13,0,1,2,3,4,5,6,7,8,9,10],[12,13,0,1,2,3,4,5,6,7,8,9,10,11]],"identity":1}。請依 [group_order, element_order_rows, all_orders_divide_group_order, certificate] 欄序回答。

查看答案與解釋(14, [[0, 14], [1, 1], [2, 14], [3, 7], [4, 14], [5, 7], [6, 14], [7, 7], [8, 2], [9, 7], [10, 14], [11, 7], [12, 14], [13, 7]], 是, complete_element_order_table_for_declared_finite_group)

Wave6第六層核對=(14, [[0, 14], [1, 1], [2, 14], [3, 7], [4, 14], [5, 7], [6, 14], [7, 7], [8, 2], [9, 7], [10, 14], [11, 7], [12, 14], [13, 7]], 是, complete_element_order_table_for_declared_finite_group)；依完整明示資料獨立重算；order-p witness必須同時驗g^p=e與所有1<=k<p皆有g^k!=e；完整有限枚舉只證指定model；composite divisor不保證是某元素的階。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261112-r01-cauchy-theorem-finite-groups-0035/)

有限群的Cauchy定理 · qf-mod43-cauchy-element-order-table · candidate





## 36. 有限群的Cauchy定理

完整有限群、prime divisor與exact element-order證書。操作=cauchy-element-order-table；資料={"group_table":[[4,5,0,1,2,3],[5,0,1,2,3,4],[0,1,2,3,4,5],[1,2,3,4,5,0],[2,3,4,5,0,1],[3,4,5,0,1,2]],"identity":2}。請依 [group_order, element_order_rows, all_orders_divide_group_order, certificate] 欄序回答。

查看答案與解釋(6, [[0, 3], [1, 6], [2, 1], [3, 6], [4, 3], [5, 2]], 是, complete_element_order_table_for_declared_finite_group)

Wave6第六層核對=(6, [[0, 3], [1, 6], [2, 1], [3, 6], [4, 3], [5, 2]], 是, complete_element_order_table_for_declared_finite_group)；依完整明示資料獨立重算；order-p witness必須同時驗g^p=e與所有1<=k<p皆有g^k!=e；完整有限枚舉只證指定model；composite divisor不保證是某元素的階。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261112-r01-cauchy-theorem-finite-groups-0036/)

有限群的Cauchy定理 · qf-mod43-cauchy-element-order-table · candidate





## 37. 有限群的Cauchy定理

完整有限群、prime divisor與exact element-order證書。操作=cauchy-element-order-table；資料={"group_table":[[6,7,0,1,2,3,4,5],[7,0,1,2,3,4,5,6],[0,1,2,3,4,5,6,7],[1,2,3,4,5,6,7,0],[2,3,4,5,6,7,0,1],[3,4,5,6,7,0,1,2],[4,5,6,7,0,1,2,3],[5,6,7,0,1,2,3,4]],"identity":2}。請依 [group_order, element_order_rows, all_orders_divide_group_order, certificate] 欄序回答。

查看答案與解釋(8, [[0, 4], [1, 8], [2, 1], [3, 8], [4, 4], [5, 8], [6, 2], [7, 8]], 是, complete_element_order_table_for_declared_finite_group)

Wave6第六層核對=(8, [[0, 4], [1, 8], [2, 1], [3, 8], [4, 4], [5, 8], [6, 2], [7, 8]], 是, complete_element_order_table_for_declared_finite_group)；依完整明示資料獨立重算；order-p witness必須同時驗g^p=e與所有1<=k<p皆有g^k!=e；完整有限枚舉只證指定model；composite divisor不保證是某元素的階。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261112-r01-cauchy-theorem-finite-groups-0037/)

有限群的Cauchy定理 · qf-mod43-cauchy-element-order-table · candidate





## 38. 有限群的Cauchy定理

完整有限群、prime divisor與exact element-order證書。操作=cauchy-element-order-table；資料={"group_table":[[8,9,0,1,2,3,4,5,6,7],[9,0,1,2,3,4,5,6,7,8],[0,1,2,3,4,5,6,7,8,9],[1,2,3,4,5,6,7,8,9,0],[2,3,4,5,6,7,8,9,0,1],[3,4,5,6,7,8,9,0,1,2],[4,5,6,7,8,9,0,1,2,3],[5,6,7,8,9,0,1,2,3,4],[6,7,8,9,0,1,2,3,4,5],[7,8,9,0,1,2,3,4,5,6]],"identity":2}。請依 [group_order, element_order_rows, all_orders_divide_group_order, certificate] 欄序回答。

查看答案與解釋(10, [[0, 5], [1, 10], [2, 1], [3, 10], [4, 5], [5, 10], [6, 5], [7, 2], [8, 5], [9, 10]], 是, complete_element_order_table_for_declared_finite_group)

Wave6第六層核對=(10, [[0, 5], [1, 10], [2, 1], [3, 10], [4, 5], [5, 10], [6, 5], [7, 2], [8, 5], [9, 10]], 是, complete_element_order_table_for_declared_finite_group)；依完整明示資料獨立重算；order-p witness必須同時驗g^p=e與所有1<=k<p皆有g^k!=e；完整有限枚舉只證指定model；composite divisor不保證是某元素的階。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261112-r01-cauchy-theorem-finite-groups-0038/)

有限群的Cauchy定理 · qf-mod43-cauchy-element-order-table · candidate





## 39. 有限群的Cauchy定理

完整有限群、prime divisor與exact element-order證書。操作=cauchy-element-order-table；資料={"group_table":[[10,11,0,1,2,3,4,5,6,7,8,9],[11,0,1,2,3,4,5,6,7,8,9,10],[0,1,2,3,4,5,6,7,8,9,10,11],[1,2,3,4,5,6,7,8,9,10,11,0],[2,3,4,5,6,7,8,9,10,11,0,1],[3,4,5,6,7,8,9,10,11,0,1,2],[4,5,6,7,8,9,10,11,0,1,2,3],[5,6,7,8,9,10,11,0,1,2,3,4],[6,7,8,9,10,11,0,1,2,3,4,5],[7,8,9,10,11,0,1,2,3,4,5,6],[8,9,10,11,0,1,2,3,4,5,6,7],[9,10,11,0,1,2,3,4,5,6,7,8]],"identity":2}。請依 [group_order, element_order_rows, all_orders_divide_group_order, certificate] 欄序回答。

查看答案與解釋(12, [[0, 6], [1, 12], [2, 1], [3, 12], [4, 6], [5, 4], [6, 3], [7, 12], [8, 2], [9, 12], [10, 3], [11, 4]], 是, complete_element_order_table_for_declared_finite_group)

Wave6第六層核對=(12, [[0, 6], [1, 12], [2, 1], [3, 12], [4, 6], [5, 4], [6, 3], [7, 12], [8, 2], [9, 12], [10, 3], [11, 4]], 是, complete_element_order_table_for_declared_finite_group)；依完整明示資料獨立重算；order-p witness必須同時驗g^p=e與所有1<=k<p皆有g^k!=e；完整有限枚舉只證指定model；composite divisor不保證是某元素的階。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261112-r01-cauchy-theorem-finite-groups-0039/)

有限群的Cauchy定理 · qf-mod43-cauchy-element-order-table · candidate





## 40. 有限群的Cauchy定理

完整有限群、prime divisor與exact element-order證書。操作=cauchy-element-order-table；資料={"group_table":[[12,13,0,1,2,3,4,5,6,7,8,9,10,11],[13,0,1,2,3,4,5,6,7,8,9,10,11,12],[0,1,2,3,4,5,6,7,8,9,10,11,12,13],[1,2,3,4,5,6,7,8,9,10,11,12,13,0],[2,3,4,5,6,7,8,9,10,11,12,13,0,1],[3,4,5,6,7,8,9,10,11,12,13,0,1,2],[4,5,6,7,8,9,10,11,12,13,0,1,2,3],[5,6,7,8,9,10,11,12,13,0,1,2,3,4],[6,7,8,9,10,11,12,13,0,1,2,3,4,5],[7,8,9,10,11,12,13,0,1,2,3,4,5,6],[8,9,10,11,12,13,0,1,2,3,4,5,6,7],[9,10,11,12,13,0,1,2,3,4,5,6,7,8],[10,11,12,13,0,1,2,3,4,5,6,7,8,9],[11,12,13,0,1,2,3,4,5,6,7,8,9,10]],"identity":2}。請依 [group_order, element_order_rows, all_orders_divide_group_order, certificate] 欄序回答。

查看答案與解釋(14, [[0, 7], [1, 14], [2, 1], [3, 14], [4, 7], [5, 14], [6, 7], [7, 14], [8, 7], [9, 2], [10, 7], [11, 14], [12, 7], [13, 14]], 是, complete_element_order_table_for_declared_finite_group)

Wave6第六層核對=(14, [[0, 7], [1, 14], [2, 1], [3, 14], [4, 7], [5, 14], [6, 7], [7, 14], [8, 7], [9, 2], [10, 7], [11, 14], [12, 7], [13, 14]], 是, complete_element_order_table_for_declared_finite_group)；依完整明示資料獨立重算；order-p witness必須同時驗g^p=e與所有1<=k<p皆有g^k!=e；完整有限枚舉只證指定model；composite divisor不保證是某元素的階。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261112-r01-cauchy-theorem-finite-groups-0040/)

有限群的Cauchy定理 · qf-mod43-cauchy-element-order-table · candidate





## 41. 有限群的Cauchy定理

完整有限群、prime divisor與exact element-order證書。操作=cauchy-element-order-table；資料={"group_table":[[3,4,5,0,1,2],[4,5,0,1,2,3],[5,0,1,2,3,4],[0,1,2,3,4,5],[1,2,3,4,5,0],[2,3,4,5,0,1]],"identity":3}。請依 [group_order, element_order_rows, all_orders_divide_group_order, certificate] 欄序回答。

查看答案與解釋(6, [[0, 2], [1, 3], [2, 6], [3, 1], [4, 6], [5, 3]], 是, complete_element_order_table_for_declared_finite_group)

Wave6第六層核對=(6, [[0, 2], [1, 3], [2, 6], [3, 1], [4, 6], [5, 3]], 是, complete_element_order_table_for_declared_finite_group)；依完整明示資料獨立重算；order-p witness必須同時驗g^p=e與所有1<=k<p皆有g^k!=e；完整有限枚舉只證指定model；composite divisor不保證是某元素的階。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261112-r01-cauchy-theorem-finite-groups-0041/)

有限群的Cauchy定理 · qf-mod43-cauchy-element-order-table · candidate





## 42. 有限群的Cauchy定理

完整有限群、prime divisor與exact element-order證書。操作=cauchy-element-order-table；資料={"group_table":[[5,6,7,0,1,2,3,4],[6,7,0,1,2,3,4,5],[7,0,1,2,3,4,5,6],[0,1,2,3,4,5,6,7],[1,2,3,4,5,6,7,0],[2,3,4,5,6,7,0,1],[3,4,5,6,7,0,1,2],[4,5,6,7,0,1,2,3]],"identity":3}。請依 [group_order, element_order_rows, all_orders_divide_group_order, certificate] 欄序回答。

查看答案與解釋(8, [[0, 8], [1, 4], [2, 8], [3, 1], [4, 8], [5, 4], [6, 8], [7, 2]], 是, complete_element_order_table_for_declared_finite_group)

Wave6第六層核對=(8, [[0, 8], [1, 4], [2, 8], [3, 1], [4, 8], [5, 4], [6, 8], [7, 2]], 是, complete_element_order_table_for_declared_finite_group)；依完整明示資料獨立重算；order-p witness必須同時驗g^p=e與所有1<=k<p皆有g^k!=e；完整有限枚舉只證指定model；composite divisor不保證是某元素的階。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261112-r01-cauchy-theorem-finite-groups-0042/)

有限群的Cauchy定理 · qf-mod43-cauchy-element-order-table · candidate





## 43. 有限群的Cauchy定理

完整有限群、prime divisor與exact element-order證書。操作=cauchy-element-order-table；資料={"group_table":[[7,8,9,0,1,2,3,4,5,6],[8,9,0,1,2,3,4,5,6,7],[9,0,1,2,3,4,5,6,7,8],[0,1,2,3,4,5,6,7,8,9],[1,2,3,4,5,6,7,8,9,0],[2,3,4,5,6,7,8,9,0,1],[3,4,5,6,7,8,9,0,1,2],[4,5,6,7,8,9,0,1,2,3],[5,6,7,8,9,0,1,2,3,4],[6,7,8,9,0,1,2,3,4,5]],"identity":3}。請依 [group_order, element_order_rows, all_orders_divide_group_order, certificate] 欄序回答。

查看答案與解釋(10, [[0, 10], [1, 5], [2, 10], [3, 1], [4, 10], [5, 5], [6, 10], [7, 5], [8, 2], [9, 5]], 是, complete_element_order_table_for_declared_finite_group)

Wave6第六層核對=(10, [[0, 10], [1, 5], [2, 10], [3, 1], [4, 10], [5, 5], [6, 10], [7, 5], [8, 2], [9, 5]], 是, complete_element_order_table_for_declared_finite_group)；依完整明示資料獨立重算；order-p witness必須同時驗g^p=e與所有1<=k<p皆有g^k!=e；完整有限枚舉只證指定model；composite divisor不保證是某元素的階。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261112-r01-cauchy-theorem-finite-groups-0043/)

有限群的Cauchy定理 · qf-mod43-cauchy-element-order-table · candidate





## 44. 有限群的Cauchy定理

完整有限群、prime divisor與exact element-order證書。操作=cauchy-element-order-table；資料={"group_table":[[9,10,11,0,1,2,3,4,5,6,7,8],[10,11,0,1,2,3,4,5,6,7,8,9],[11,0,1,2,3,4,5,6,7,8,9,10],[0,1,2,3,4,5,6,7,8,9,10,11],[1,2,3,4,5,6,7,8,9,10,11,0],[2,3,4,5,6,7,8,9,10,11,0,1],[3,4,5,6,7,8,9,10,11,0,1,2],[4,5,6,7,8,9,10,11,0,1,2,3],[5,6,7,8,9,10,11,0,1,2,3,4],[6,7,8,9,10,11,0,1,2,3,4,5],[7,8,9,10,11,0,1,2,3,4,5,6],[8,9,10,11,0,1,2,3,4,5,6,7]],"identity":3}。請依 [group_order, element_order_rows, all_orders_divide_group_order, certificate] 欄序回答。

查看答案與解釋(12, [[0, 4], [1, 6], [2, 12], [3, 1], [4, 12], [5, 6], [6, 4], [7, 3], [8, 12], [9, 2], [10, 12], [11, 3]], 是, complete_element_order_table_for_declared_finite_group)

Wave6第六層核對=(12, [[0, 4], [1, 6], [2, 12], [3, 1], [4, 12], [5, 6], [6, 4], [7, 3], [8, 12], [9, 2], [10, 12], [11, 3]], 是, complete_element_order_table_for_declared_finite_group)；依完整明示資料獨立重算；order-p witness必須同時驗g^p=e與所有1<=k<p皆有g^k!=e；完整有限枚舉只證指定model；composite divisor不保證是某元素的階。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261112-r01-cauchy-theorem-finite-groups-0044/)

有限群的Cauchy定理 · qf-mod43-cauchy-element-order-table · candidate





## 45. 有限群的Cauchy定理

完整有限群、prime divisor與exact element-order證書。操作=cauchy-element-order-table；資料={"group_table":[[11,12,13,0,1,2,3,4,5,6,7,8,9,10],[12,13,0,1,2,3,4,5,6,7,8,9,10,11],[13,0,1,2,3,4,5,6,7,8,9,10,11,12],[0,1,2,3,4,5,6,7,8,9,10,11,12,13],[1,2,3,4,5,6,7,8,9,10,11,12,13,0],[2,3,4,5,6,7,8,9,10,11,12,13,0,1],[3,4,5,6,7,8,9,10,11,12,13,0,1,2],[4,5,6,7,8,9,10,11,12,13,0,1,2,3],[5,6,7,8,9,10,11,12,13,0,1,2,3,4],[6,7,8,9,10,11,12,13,0,1,2,3,4,5],[7,8,9,10,11,12,13,0,1,2,3,4,5,6],[8,9,10,11,12,13,0,1,2,3,4,5,6,7],[9,10,11,12,13,0,1,2,3,4,5,6,7,8],[10,11,12,13,0,1,2,3,4,5,6,7,8,9]],"identity":3}。請依 [group_order, element_order_rows, all_orders_divide_group_order, certificate] 欄序回答。

查看答案與解釋(14, [[0, 14], [1, 7], [2, 14], [3, 1], [4, 14], [5, 7], [6, 14], [7, 7], [8, 14], [9, 7], [10, 2], [11, 7], [12, 14], [13, 7]], 是, complete_element_order_table_for_declared_finite_group)

Wave6第六層核對=(14, [[0, 14], [1, 7], [2, 14], [3, 1], [4, 14], [5, 7], [6, 14], [7, 7], [8, 14], [9, 7], [10, 2], [11, 7], [12, 14], [13, 7]], 是, complete_element_order_table_for_declared_finite_group)；依完整明示資料獨立重算；order-p witness必須同時驗g^p=e與所有1<=k<p皆有g^k!=e；完整有限枚舉只證指定model；composite divisor不保證是某元素的階。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261112-r01-cauchy-theorem-finite-groups-0045/)

有限群的Cauchy定理 · qf-mod43-cauchy-element-order-table · candidate





## 46. 有限群的Cauchy定理

完整有限群、prime divisor與exact element-order證書。操作=cauchy-element-order-table；資料={"group_table":[[2,3,4,5,0,1],[3,4,5,0,1,2],[4,5,0,1,2,3],[5,0,1,2,3,4],[0,1,2,3,4,5],[1,2,3,4,5,0]],"identity":4}。請依 [group_order, element_order_rows, all_orders_divide_group_order, certificate] 欄序回答。

查看答案與解釋(6, [[0, 3], [1, 2], [2, 3], [3, 6], [4, 1], [5, 6]], 是, complete_element_order_table_for_declared_finite_group)

Wave6第六層核對=(6, [[0, 3], [1, 2], [2, 3], [3, 6], [4, 1], [5, 6]], 是, complete_element_order_table_for_declared_finite_group)；依完整明示資料獨立重算；order-p witness必須同時驗g^p=e與所有1<=k<p皆有g^k!=e；完整有限枚舉只證指定model；composite divisor不保證是某元素的階。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261112-r01-cauchy-theorem-finite-groups-0046/)

有限群的Cauchy定理 · qf-mod43-cauchy-element-order-table · candidate





## 47. 有限群的Cauchy定理

完整有限群、prime divisor與exact element-order證書。操作=cauchy-element-order-table；資料={"group_table":[[4,5,6,7,0,1,2,3],[5,6,7,0,1,2,3,4],[6,7,0,1,2,3,4,5],[7,0,1,2,3,4,5,6],[0,1,2,3,4,5,6,7],[1,2,3,4,5,6,7,0],[2,3,4,5,6,7,0,1],[3,4,5,6,7,0,1,2]],"identity":4}。請依 [group_order, element_order_rows, all_orders_divide_group_order, certificate] 欄序回答。

查看答案與解釋(8, [[0, 2], [1, 8], [2, 4], [3, 8], [4, 1], [5, 8], [6, 4], [7, 8]], 是, complete_element_order_table_for_declared_finite_group)

Wave6第六層核對=(8, [[0, 2], [1, 8], [2, 4], [3, 8], [4, 1], [5, 8], [6, 4], [7, 8]], 是, complete_element_order_table_for_declared_finite_group)；依完整明示資料獨立重算；order-p witness必須同時驗g^p=e與所有1<=k<p皆有g^k!=e；完整有限枚舉只證指定model；composite divisor不保證是某元素的階。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261112-r01-cauchy-theorem-finite-groups-0047/)

有限群的Cauchy定理 · qf-mod43-cauchy-element-order-table · candidate





## 48. 有限群的Cauchy定理

完整有限群、prime divisor與exact element-order證書。操作=cauchy-element-order-table；資料={"group_table":[[6,7,8,9,0,1,2,3,4,5],[7,8,9,0,1,2,3,4,5,6],[8,9,0,1,2,3,4,5,6,7],[9,0,1,2,3,4,5,6,7,8],[0,1,2,3,4,5,6,7,8,9],[1,2,3,4,5,6,7,8,9,0],[2,3,4,5,6,7,8,9,0,1],[3,4,5,6,7,8,9,0,1,2],[4,5,6,7,8,9,0,1,2,3],[5,6,7,8,9,0,1,2,3,4]],"identity":4}。請依 [group_order, element_order_rows, all_orders_divide_group_order, certificate] 欄序回答。

查看答案與解釋(10, [[0, 5], [1, 10], [2, 5], [3, 10], [4, 1], [5, 10], [6, 5], [7, 10], [8, 5], [9, 2]], 是, complete_element_order_table_for_declared_finite_group)

Wave6第六層核對=(10, [[0, 5], [1, 10], [2, 5], [3, 10], [4, 1], [5, 10], [6, 5], [7, 10], [8, 5], [9, 2]], 是, complete_element_order_table_for_declared_finite_group)；依完整明示資料獨立重算；order-p witness必須同時驗g^p=e與所有1<=k<p皆有g^k!=e；完整有限枚舉只證指定model；composite divisor不保證是某元素的階。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261112-r01-cauchy-theorem-finite-groups-0048/)

有限群的Cauchy定理 · qf-mod43-cauchy-element-order-table · candidate





## 49. 有限群的Cauchy定理

完整有限群、prime divisor與exact element-order證書。操作=cauchy-element-order-table；資料={"group_table":[[8,9,10,11,0,1,2,3,4,5,6,7],[9,10,11,0,1,2,3,4,5,6,7,8],[10,11,0,1,2,3,4,5,6,7,8,9],[11,0,1,2,3,4,5,6,7,8,9,10],[0,1,2,3,4,5,6,7,8,9,10,11],[1,2,3,4,5,6,7,8,9,10,11,0],[2,3,4,5,6,7,8,9,10,11,0,1],[3,4,5,6,7,8,9,10,11,0,1,2],[4,5,6,7,8,9,10,11,0,1,2,3],[5,6,7,8,9,10,11,0,1,2,3,4],[6,7,8,9,10,11,0,1,2,3,4,5],[7,8,9,10,11,0,1,2,3,4,5,6]],"identity":4}。請依 [group_order, element_order_rows, all_orders_divide_group_order, certificate] 欄序回答。

查看答案與解釋(12, [[0, 3], [1, 4], [2, 6], [3, 12], [4, 1], [5, 12], [6, 6], [7, 4], [8, 3], [9, 12], [10, 2], [11, 12]], 是, complete_element_order_table_for_declared_finite_group)

Wave6第六層核對=(12, [[0, 3], [1, 4], [2, 6], [3, 12], [4, 1], [5, 12], [6, 6], [7, 4], [8, 3], [9, 12], [10, 2], [11, 12]], 是, complete_element_order_table_for_declared_finite_group)；依完整明示資料獨立重算；order-p witness必須同時驗g^p=e與所有1<=k<p皆有g^k!=e；完整有限枚舉只證指定model；composite divisor不保證是某元素的階。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261112-r01-cauchy-theorem-finite-groups-0049/)

有限群的Cauchy定理 · qf-mod43-cauchy-element-order-table · candidate





## 50. 有限群的Cauchy定理

完整有限群、prime divisor與exact element-order證書。操作=cauchy-element-order-table；資料={"group_table":[[10,11,12,13,0,1,2,3,4,5,6,7,8,9],[11,12,13,0,1,2,3,4,5,6,7,8,9,10],[12,13,0,1,2,3,4,5,6,7,8,9,10,11],[13,0,1,2,3,4,5,6,7,8,9,10,11,12],[0,1,2,3,4,5,6,7,8,9,10,11,12,13],[1,2,3,4,5,6,7,8,9,10,11,12,13,0],[2,3,4,5,6,7,8,9,10,11,12,13,0,1],[3,4,5,6,7,8,9,10,11,12,13,0,1,2],[4,5,6,7,8,9,10,11,12,13,0,1,2,3],[5,6,7,8,9,10,11,12,13,0,1,2,3,4],[6,7,8,9,10,11,12,13,0,1,2,3,4,5],[7,8,9,10,11,12,13,0,1,2,3,4,5,6],[8,9,10,11,12,13,0,1,2,3,4,5,6,7],[9,10,11,12,13,0,1,2,3,4,5,6,7,8]],"identity":4}。請依 [group_order, element_order_rows, all_orders_divide_group_order, certificate] 欄序回答。

查看答案與解釋(14, [[0, 7], [1, 14], [2, 7], [3, 14], [4, 1], [5, 14], [6, 7], [7, 14], [8, 7], [9, 14], [10, 7], [11, 2], [12, 7], [13, 14]], 是, complete_element_order_table_for_declared_finite_group)

Wave6第六層核對=(14, [[0, 7], [1, 14], [2, 7], [3, 14], [4, 1], [5, 14], [6, 7], [7, 14], [8, 7], [9, 14], [10, 7], [11, 2], [12, 7], [13, 14]], 是, complete_element_order_table_for_declared_finite_group)；依完整明示資料獨立重算；order-p witness必須同時驗g^p=e與所有1<=k<p皆有g^k!=e；完整有限枚舉只證指定model；composite divisor不保證是某元素的階。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261112-r01-cauchy-theorem-finite-groups-0050/)

有限群的Cauchy定理 · qf-mod43-cauchy-element-order-table · candidate





## 51. 有限群的Cauchy定理

完整有限群、prime divisor與exact element-order證書。操作=cauchy-order-p-witness；資料={"group_table":[[0,1,2,3,4,5],[1,2,3,4,5,0],[2,3,4,5,0,1],[3,4,5,0,1,2],[4,5,0,1,2,3],[5,0,1,2,3,4]],"identity":0,"prime":2,"element":3}。請依 [group_order, prime, element, positive_power_rows, p_power_is_identity, no_smaller_positive_identity_power, certificate] 欄序回答。

g^p=e與所有較小正冪不等於e須分開核；identity雖滿足g^p=e，卻不是order-p witness。

查看答案與解釋(6, 2, 3, [[1, 3], [2, 0]], 是, 是, g_to_p_is_identity_and_no_smaller_positive_power_is)

Wave6第六層核對=(6, 2, 3, [[1, 3], [2, 0]], 是, 是, g_to_p_is_identity_and_no_smaller_positive_power_is)；依完整明示資料獨立重算；order-p witness必須同時驗g^p=e與所有1<=k<p皆有g^k!=e；完整有限枚舉只證指定model；composite divisor不保證是某元素的階。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261112-r01-cauchy-theorem-finite-groups-0051/)

有限群的Cauchy定理 · qf-mod43-cauchy-order-p-witness · candidate





## 52. 有限群的Cauchy定理

完整有限群、prime divisor與exact element-order證書。操作=cauchy-order-p-witness；資料={"group_table":[[0,1,2,3,4,5,6,7],[1,2,3,4,5,6,7,0],[2,3,4,5,6,7,0,1],[3,4,5,6,7,0,1,2],[4,5,6,7,0,1,2,3],[5,6,7,0,1,2,3,4],[6,7,0,1,2,3,4,5],[7,0,1,2,3,4,5,6]],"identity":0,"prime":2,"element":4}。請依 [group_order, prime, element, positive_power_rows, p_power_is_identity, no_smaller_positive_identity_power, certificate] 欄序回答。

g^p=e與所有較小正冪不等於e須分開核；identity雖滿足g^p=e，卻不是order-p witness。

查看答案與解釋(8, 2, 4, [[1, 4], [2, 0]], 是, 是, g_to_p_is_identity_and_no_smaller_positive_power_is)

Wave6第六層核對=(8, 2, 4, [[1, 4], [2, 0]], 是, 是, g_to_p_is_identity_and_no_smaller_positive_power_is)；依完整明示資料獨立重算；order-p witness必須同時驗g^p=e與所有1<=k<p皆有g^k!=e；完整有限枚舉只證指定model；composite divisor不保證是某元素的階。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261112-r01-cauchy-theorem-finite-groups-0052/)

有限群的Cauchy定理 · qf-mod43-cauchy-order-p-witness · candidate





## 53. 有限群的Cauchy定理

完整有限群、prime divisor與exact element-order證書。操作=cauchy-order-p-witness；資料={"group_table":[[0,1,2,3,4,5,6,7,8,9],[1,2,3,4,5,6,7,8,9,0],[2,3,4,5,6,7,8,9,0,1],[3,4,5,6,7,8,9,0,1,2],[4,5,6,7,8,9,0,1,2,3],[5,6,7,8,9,0,1,2,3,4],[6,7,8,9,0,1,2,3,4,5],[7,8,9,0,1,2,3,4,5,6],[8,9,0,1,2,3,4,5,6,7],[9,0,1,2,3,4,5,6,7,8]],"identity":0,"prime":2,"element":5}。請依 [group_order, prime, element, positive_power_rows, p_power_is_identity, no_smaller_positive_identity_power, certificate] 欄序回答。

g^p=e與所有較小正冪不等於e須分開核；identity雖滿足g^p=e，卻不是order-p witness。

查看答案與解釋(10, 2, 5, [[1, 5], [2, 0]], 是, 是, g_to_p_is_identity_and_no_smaller_positive_power_is)

Wave6第六層核對=(10, 2, 5, [[1, 5], [2, 0]], 是, 是, g_to_p_is_identity_and_no_smaller_positive_power_is)；依完整明示資料獨立重算；order-p witness必須同時驗g^p=e與所有1<=k<p皆有g^k!=e；完整有限枚舉只證指定model；composite divisor不保證是某元素的階。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261112-r01-cauchy-theorem-finite-groups-0053/)

有限群的Cauchy定理 · qf-mod43-cauchy-order-p-witness · candidate





## 54. 有限群的Cauchy定理

完整有限群、prime divisor與exact element-order證書。操作=cauchy-order-p-witness；資料={"group_table":[[0,1,2,3,4,5,6,7,8,9,10,11],[1,2,3,4,5,6,7,8,9,10,11,0],[2,3,4,5,6,7,8,9,10,11,0,1],[3,4,5,6,7,8,9,10,11,0,1,2],[4,5,6,7,8,9,10,11,0,1,2,3],[5,6,7,8,9,10,11,0,1,2,3,4],[6,7,8,9,10,11,0,1,2,3,4,5],[7,8,9,10,11,0,1,2,3,4,5,6],[8,9,10,11,0,1,2,3,4,5,6,7],[9,10,11,0,1,2,3,4,5,6,7,8],[10,11,0,1,2,3,4,5,6,7,8,9],[11,0,1,2,3,4,5,6,7,8,9,10]],"identity":0,"prime":2,"element":6}。請依 [group_order, prime, element, positive_power_rows, p_power_is_identity, no_smaller_positive_identity_power, certificate] 欄序回答。

g^p=e與所有較小正冪不等於e須分開核；identity雖滿足g^p=e，卻不是order-p witness。

查看答案與解釋(12, 2, 6, [[1, 6], [2, 0]], 是, 是, g_to_p_is_identity_and_no_smaller_positive_power_is)

Wave6第六層核對=(12, 2, 6, [[1, 6], [2, 0]], 是, 是, g_to_p_is_identity_and_no_smaller_positive_power_is)；依完整明示資料獨立重算；order-p witness必須同時驗g^p=e與所有1<=k<p皆有g^k!=e；完整有限枚舉只證指定model；composite divisor不保證是某元素的階。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261112-r01-cauchy-theorem-finite-groups-0054/)

有限群的Cauchy定理 · qf-mod43-cauchy-order-p-witness · candidate





## 55. 有限群的Cauchy定理

完整有限群、prime divisor與exact element-order證書。操作=cauchy-order-p-witness；資料={"group_table":[[0,1,2,3,4,5,6,7,8,9,10,11,12,13],[1,2,3,4,5,6,7,8,9,10,11,12,13,0],[2,3,4,5,6,7,8,9,10,11,12,13,0,1],[3,4,5,6,7,8,9,10,11,12,13,0,1,2],[4,5,6,7,8,9,10,11,12,13,0,1,2,3],[5,6,7,8,9,10,11,12,13,0,1,2,3,4],[6,7,8,9,10,11,12,13,0,1,2,3,4,5],[7,8,9,10,11,12,13,0,1,2,3,4,5,6],[8,9,10,11,12,13,0,1,2,3,4,5,6,7],[9,10,11,12,13,0,1,2,3,4,5,6,7,8],[10,11,12,13,0,1,2,3,4,5,6,7,8,9],[11,12,13,0,1,2,3,4,5,6,7,8,9,10],[12,13,0,1,2,3,4,5,6,7,8,9,10,11],[13,0,1,2,3,4,5,6,7,8,9,10,11,12]],"identity":0,"prime":2,"element":7}。請依 [group_order, prime, element, positive_power_rows, p_power_is_identity, no_smaller_positive_identity_power, certificate] 欄序回答。

g^p=e與所有較小正冪不等於e須分開核；identity雖滿足g^p=e，卻不是order-p witness。

查看答案與解釋(14, 2, 7, [[1, 7], [2, 0]], 是, 是, g_to_p_is_identity_and_no_smaller_positive_power_is)

Wave6第六層核對=(14, 2, 7, [[1, 7], [2, 0]], 是, 是, g_to_p_is_identity_and_no_smaller_positive_power_is)；依完整明示資料獨立重算；order-p witness必須同時驗g^p=e與所有1<=k<p皆有g^k!=e；完整有限枚舉只證指定model；composite divisor不保證是某元素的階。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261112-r01-cauchy-theorem-finite-groups-0055/)

有限群的Cauchy定理 · qf-mod43-cauchy-order-p-witness · candidate





## 56. 有限群的Cauchy定理

完整有限群、prime divisor與exact element-order證書。操作=cauchy-order-p-witness；資料={"group_table":[[5,0,1,2,3,4],[0,1,2,3,4,5],[1,2,3,4,5,0],[2,3,4,5,0,1],[3,4,5,0,1,2],[4,5,0,1,2,3]],"identity":1,"prime":2,"element":4}。請依 [group_order, prime, element, positive_power_rows, p_power_is_identity, no_smaller_positive_identity_power, certificate] 欄序回答。

g^p=e與所有較小正冪不等於e須分開核；identity雖滿足g^p=e，卻不是order-p witness。

查看答案與解釋(6, 2, 4, [[1, 4], [2, 1]], 是, 是, g_to_p_is_identity_and_no_smaller_positive_power_is)

Wave6第六層核對=(6, 2, 4, [[1, 4], [2, 1]], 是, 是, g_to_p_is_identity_and_no_smaller_positive_power_is)；依完整明示資料獨立重算；order-p witness必須同時驗g^p=e與所有1<=k<p皆有g^k!=e；完整有限枚舉只證指定model；composite divisor不保證是某元素的階。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261112-r01-cauchy-theorem-finite-groups-0056/)

有限群的Cauchy定理 · qf-mod43-cauchy-order-p-witness · candidate





## 57. 有限群的Cauchy定理

完整有限群、prime divisor與exact element-order證書。操作=cauchy-order-p-witness；資料={"group_table":[[7,0,1,2,3,4,5,6],[0,1,2,3,4,5,6,7],[1,2,3,4,5,6,7,0],[2,3,4,5,6,7,0,1],[3,4,5,6,7,0,1,2],[4,5,6,7,0,1,2,3],[5,6,7,0,1,2,3,4],[6,7,0,1,2,3,4,5]],"identity":1,"prime":2,"element":5}。請依 [group_order, prime, element, positive_power_rows, p_power_is_identity, no_smaller_positive_identity_power, certificate] 欄序回答。

g^p=e與所有較小正冪不等於e須分開核；identity雖滿足g^p=e，卻不是order-p witness。

查看答案與解釋(8, 2, 5, [[1, 5], [2, 1]], 是, 是, g_to_p_is_identity_and_no_smaller_positive_power_is)

Wave6第六層核對=(8, 2, 5, [[1, 5], [2, 1]], 是, 是, g_to_p_is_identity_and_no_smaller_positive_power_is)；依完整明示資料獨立重算；order-p witness必須同時驗g^p=e與所有1<=k<p皆有g^k!=e；完整有限枚舉只證指定model；composite divisor不保證是某元素的階。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261112-r01-cauchy-theorem-finite-groups-0057/)

有限群的Cauchy定理 · qf-mod43-cauchy-order-p-witness · candidate





## 58. 有限群的Cauchy定理

完整有限群、prime divisor與exact element-order證書。操作=cauchy-order-p-witness；資料={"group_table":[[9,0,1,2,3,4,5,6,7,8],[0,1,2,3,4,5,6,7,8,9],[1,2,3,4,5,6,7,8,9,0],[2,3,4,5,6,7,8,9,0,1],[3,4,5,6,7,8,9,0,1,2],[4,5,6,7,8,9,0,1,2,3],[5,6,7,8,9,0,1,2,3,4],[6,7,8,9,0,1,2,3,4,5],[7,8,9,0,1,2,3,4,5,6],[8,9,0,1,2,3,4,5,6,7]],"identity":1,"prime":2,"element":6}。請依 [group_order, prime, element, positive_power_rows, p_power_is_identity, no_smaller_positive_identity_power, certificate] 欄序回答。

g^p=e與所有較小正冪不等於e須分開核；identity雖滿足g^p=e，卻不是order-p witness。

查看答案與解釋(10, 2, 6, [[1, 6], [2, 1]], 是, 是, g_to_p_is_identity_and_no_smaller_positive_power_is)

Wave6第六層核對=(10, 2, 6, [[1, 6], [2, 1]], 是, 是, g_to_p_is_identity_and_no_smaller_positive_power_is)；依完整明示資料獨立重算；order-p witness必須同時驗g^p=e與所有1<=k<p皆有g^k!=e；完整有限枚舉只證指定model；composite divisor不保證是某元素的階。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261112-r01-cauchy-theorem-finite-groups-0058/)

有限群的Cauchy定理 · qf-mod43-cauchy-order-p-witness · candidate





## 59. 有限群的Cauchy定理

完整有限群、prime divisor與exact element-order證書。操作=cauchy-order-p-witness；資料={"group_table":[[11,0,1,2,3,4,5,6,7,8,9,10],[0,1,2,3,4,5,6,7,8,9,10,11],[1,2,3,4,5,6,7,8,9,10,11,0],[2,3,4,5,6,7,8,9,10,11,0,1],[3,4,5,6,7,8,9,10,11,0,1,2],[4,5,6,7,8,9,10,11,0,1,2,3],[5,6,7,8,9,10,11,0,1,2,3,4],[6,7,8,9,10,11,0,1,2,3,4,5],[7,8,9,10,11,0,1,2,3,4,5,6],[8,9,10,11,0,1,2,3,4,5,6,7],[9,10,11,0,1,2,3,4,5,6,7,8],[10,11,0,1,2,3,4,5,6,7,8,9]],"identity":1,"prime":2,"element":7}。請依 [group_order, prime, element, positive_power_rows, p_power_is_identity, no_smaller_positive_identity_power, certificate] 欄序回答。

g^p=e與所有較小正冪不等於e須分開核；identity雖滿足g^p=e，卻不是order-p witness。

查看答案與解釋(12, 2, 7, [[1, 7], [2, 1]], 是, 是, g_to_p_is_identity_and_no_smaller_positive_power_is)

Wave6第六層核對=(12, 2, 7, [[1, 7], [2, 1]], 是, 是, g_to_p_is_identity_and_no_smaller_positive_power_is)；依完整明示資料獨立重算；order-p witness必須同時驗g^p=e與所有1<=k<p皆有g^k!=e；完整有限枚舉只證指定model；composite divisor不保證是某元素的階。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261112-r01-cauchy-theorem-finite-groups-0059/)

有限群的Cauchy定理 · qf-mod43-cauchy-order-p-witness · candidate





## 60. 有限群的Cauchy定理

完整有限群、prime divisor與exact element-order證書。操作=cauchy-order-p-witness；資料={"group_table":[[13,0,1,2,3,4,5,6,7,8,9,10,11,12],[0,1,2,3,4,5,6,7,8,9,10,11,12,13],[1,2,3,4,5,6,7,8,9,10,11,12,13,0],[2,3,4,5,6,7,8,9,10,11,12,13,0,1],[3,4,5,6,7,8,9,10,11,12,13,0,1,2],[4,5,6,7,8,9,10,11,12,13,0,1,2,3],[5,6,7,8,9,10,11,12,13,0,1,2,3,4],[6,7,8,9,10,11,12,13,0,1,2,3,4,5],[7,8,9,10,11,12,13,0,1,2,3,4,5,6],[8,9,10,11,12,13,0,1,2,3,4,5,6,7],[9,10,11,12,13,0,1,2,3,4,5,6,7,8],[10,11,12,13,0,1,2,3,4,5,6,7,8,9],[11,12,13,0,1,2,3,4,5,6,7,8,9,10],[12,13,0,1,2,3,4,5,6,7,8,9,10,11]],"identity":1,"prime":2,"element":8}。請依 [group_order, prime, element, positive_power_rows, p_power_is_identity, no_smaller_positive_identity_power, certificate] 欄序回答。

g^p=e與所有較小正冪不等於e須分開核；identity雖滿足g^p=e，卻不是order-p witness。

查看答案與解釋(14, 2, 8, [[1, 8], [2, 1]], 是, 是, g_to_p_is_identity_and_no_smaller_positive_power_is)

Wave6第六層核對=(14, 2, 8, [[1, 8], [2, 1]], 是, 是, g_to_p_is_identity_and_no_smaller_positive_power_is)；依完整明示資料獨立重算；order-p witness必須同時驗g^p=e與所有1<=k<p皆有g^k!=e；完整有限枚舉只證指定model；composite divisor不保證是某元素的階。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261112-r01-cauchy-theorem-finite-groups-0060/)

有限群的Cauchy定理 · qf-mod43-cauchy-order-p-witness · candidate





## 61. 有限群的Cauchy定理

完整有限群、prime divisor與exact element-order證書。操作=cauchy-order-p-witness；資料={"group_table":[[4,5,0,1,2,3],[5,0,1,2,3,4],[0,1,2,3,4,5],[1,2,3,4,5,0],[2,3,4,5,0,1],[3,4,5,0,1,2]],"identity":2,"prime":2,"element":5}。請依 [group_order, prime, element, positive_power_rows, p_power_is_identity, no_smaller_positive_identity_power, certificate] 欄序回答。

g^p=e與所有較小正冪不等於e須分開核；identity雖滿足g^p=e，卻不是order-p witness。

查看答案與解釋(6, 2, 5, [[1, 5], [2, 2]], 是, 是, g_to_p_is_identity_and_no_smaller_positive_power_is)

Wave6第六層核對=(6, 2, 5, [[1, 5], [2, 2]], 是, 是, g_to_p_is_identity_and_no_smaller_positive_power_is)；依完整明示資料獨立重算；order-p witness必須同時驗g^p=e與所有1<=k<p皆有g^k!=e；完整有限枚舉只證指定model；composite divisor不保證是某元素的階。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261112-r01-cauchy-theorem-finite-groups-0061/)

有限群的Cauchy定理 · qf-mod43-cauchy-order-p-witness · candidate





## 62. 有限群的Cauchy定理

完整有限群、prime divisor與exact element-order證書。操作=cauchy-order-p-witness；資料={"group_table":[[6,7,0,1,2,3,4,5],[7,0,1,2,3,4,5,6],[0,1,2,3,4,5,6,7],[1,2,3,4,5,6,7,0],[2,3,4,5,6,7,0,1],[3,4,5,6,7,0,1,2],[4,5,6,7,0,1,2,3],[5,6,7,0,1,2,3,4]],"identity":2,"prime":2,"element":6}。請依 [group_order, prime, element, positive_power_rows, p_power_is_identity, no_smaller_positive_identity_power, certificate] 欄序回答。

g^p=e與所有較小正冪不等於e須分開核；identity雖滿足g^p=e，卻不是order-p witness。

查看答案與解釋(8, 2, 6, [[1, 6], [2, 2]], 是, 是, g_to_p_is_identity_and_no_smaller_positive_power_is)

Wave6第六層核對=(8, 2, 6, [[1, 6], [2, 2]], 是, 是, g_to_p_is_identity_and_no_smaller_positive_power_is)；依完整明示資料獨立重算；order-p witness必須同時驗g^p=e與所有1<=k<p皆有g^k!=e；完整有限枚舉只證指定model；composite divisor不保證是某元素的階。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261112-r01-cauchy-theorem-finite-groups-0062/)

有限群的Cauchy定理 · qf-mod43-cauchy-order-p-witness · candidate





## 63. 有限群的Cauchy定理

完整有限群、prime divisor與exact element-order證書。操作=cauchy-order-p-witness；資料={"group_table":[[8,9,0,1,2,3,4,5,6,7],[9,0,1,2,3,4,5,6,7,8],[0,1,2,3,4,5,6,7,8,9],[1,2,3,4,5,6,7,8,9,0],[2,3,4,5,6,7,8,9,0,1],[3,4,5,6,7,8,9,0,1,2],[4,5,6,7,8,9,0,1,2,3],[5,6,7,8,9,0,1,2,3,4],[6,7,8,9,0,1,2,3,4,5],[7,8,9,0,1,2,3,4,5,6]],"identity":2,"prime":2,"element":7}。請依 [group_order, prime, element, positive_power_rows, p_power_is_identity, no_smaller_positive_identity_power, certificate] 欄序回答。

g^p=e與所有較小正冪不等於e須分開核；identity雖滿足g^p=e，卻不是order-p witness。

查看答案與解釋(10, 2, 7, [[1, 7], [2, 2]], 是, 是, g_to_p_is_identity_and_no_smaller_positive_power_is)

Wave6第六層核對=(10, 2, 7, [[1, 7], [2, 2]], 是, 是, g_to_p_is_identity_and_no_smaller_positive_power_is)；依完整明示資料獨立重算；order-p witness必須同時驗g^p=e與所有1<=k<p皆有g^k!=e；完整有限枚舉只證指定model；composite divisor不保證是某元素的階。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261112-r01-cauchy-theorem-finite-groups-0063/)

有限群的Cauchy定理 · qf-mod43-cauchy-order-p-witness · candidate





## 64. 有限群的Cauchy定理

完整有限群、prime divisor與exact element-order證書。操作=cauchy-order-p-witness；資料={"group_table":[[10,11,0,1,2,3,4,5,6,7,8,9],[11,0,1,2,3,4,5,6,7,8,9,10],[0,1,2,3,4,5,6,7,8,9,10,11],[1,2,3,4,5,6,7,8,9,10,11,0],[2,3,4,5,6,7,8,9,10,11,0,1],[3,4,5,6,7,8,9,10,11,0,1,2],[4,5,6,7,8,9,10,11,0,1,2,3],[5,6,7,8,9,10,11,0,1,2,3,4],[6,7,8,9,10,11,0,1,2,3,4,5],[7,8,9,10,11,0,1,2,3,4,5,6],[8,9,10,11,0,1,2,3,4,5,6,7],[9,10,11,0,1,2,3,4,5,6,7,8]],"identity":2,"prime":2,"element":8}。請依 [group_order, prime, element, positive_power_rows, p_power_is_identity, no_smaller_positive_identity_power, certificate] 欄序回答。

g^p=e與所有較小正冪不等於e須分開核；identity雖滿足g^p=e，卻不是order-p witness。

查看答案與解釋(12, 2, 8, [[1, 8], [2, 2]], 是, 是, g_to_p_is_identity_and_no_smaller_positive_power_is)

Wave6第六層核對=(12, 2, 8, [[1, 8], [2, 2]], 是, 是, g_to_p_is_identity_and_no_smaller_positive_power_is)；依完整明示資料獨立重算；order-p witness必須同時驗g^p=e與所有1<=k<p皆有g^k!=e；完整有限枚舉只證指定model；composite divisor不保證是某元素的階。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261112-r01-cauchy-theorem-finite-groups-0064/)

有限群的Cauchy定理 · qf-mod43-cauchy-order-p-witness · candidate





## 65. 有限群的Cauchy定理

完整有限群、prime divisor與exact element-order證書。操作=cauchy-order-p-witness；資料={"group_table":[[12,13,0,1,2,3,4,5,6,7,8,9,10,11],[13,0,1,2,3,4,5,6,7,8,9,10,11,12],[0,1,2,3,4,5,6,7,8,9,10,11,12,13],[1,2,3,4,5,6,7,8,9,10,11,12,13,0],[2,3,4,5,6,7,8,9,10,11,12,13,0,1],[3,4,5,6,7,8,9,10,11,12,13,0,1,2],[4,5,6,7,8,9,10,11,12,13,0,1,2,3],[5,6,7,8,9,10,11,12,13,0,1,2,3,4],[6,7,8,9,10,11,12,13,0,1,2,3,4,5],[7,8,9,10,11,12,13,0,1,2,3,4,5,6],[8,9,10,11,12,13,0,1,2,3,4,5,6,7],[9,10,11,12,13,0,1,2,3,4,5,6,7,8],[10,11,12,13,0,1,2,3,4,5,6,7,8,9],[11,12,13,0,1,2,3,4,5,6,7,8,9,10]],"identity":2,"prime":2,"element":9}。請依 [group_order, prime, element, positive_power_rows, p_power_is_identity, no_smaller_positive_identity_power, certificate] 欄序回答。

g^p=e與所有較小正冪不等於e須分開核；identity雖滿足g^p=e，卻不是order-p witness。

查看答案與解釋(14, 2, 9, [[1, 9], [2, 2]], 是, 是, g_to_p_is_identity_and_no_smaller_positive_power_is)

Wave6第六層核對=(14, 2, 9, [[1, 9], [2, 2]], 是, 是, g_to_p_is_identity_and_no_smaller_positive_power_is)；依完整明示資料獨立重算；order-p witness必須同時驗g^p=e與所有1<=k<p皆有g^k!=e；完整有限枚舉只證指定model；composite divisor不保證是某元素的階。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261112-r01-cauchy-theorem-finite-groups-0065/)

有限群的Cauchy定理 · qf-mod43-cauchy-order-p-witness · candidate





## 66. 有限群的Cauchy定理

完整有限群、prime divisor與exact element-order證書。操作=cauchy-order-p-witness；資料={"group_table":[[3,4,5,0,1,2],[4,5,0,1,2,3],[5,0,1,2,3,4],[0,1,2,3,4,5],[1,2,3,4,5,0],[2,3,4,5,0,1]],"identity":3,"prime":2,"element":0}。請依 [group_order, prime, element, positive_power_rows, p_power_is_identity, no_smaller_positive_identity_power, certificate] 欄序回答。

g^p=e與所有較小正冪不等於e須分開核；identity雖滿足g^p=e，卻不是order-p witness。

查看答案與解釋(6, 2, 0, [[1, 0], [2, 3]], 是, 是, g_to_p_is_identity_and_no_smaller_positive_power_is)

Wave6第六層核對=(6, 2, 0, [[1, 0], [2, 3]], 是, 是, g_to_p_is_identity_and_no_smaller_positive_power_is)；依完整明示資料獨立重算；order-p witness必須同時驗g^p=e與所有1<=k<p皆有g^k!=e；完整有限枚舉只證指定model；composite divisor不保證是某元素的階。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261112-r01-cauchy-theorem-finite-groups-0066/)

有限群的Cauchy定理 · qf-mod43-cauchy-order-p-witness · candidate





## 67. 有限群的Cauchy定理

完整有限群、prime divisor與exact element-order證書。操作=cauchy-order-p-witness；資料={"group_table":[[5,6,7,0,1,2,3,4],[6,7,0,1,2,3,4,5],[7,0,1,2,3,4,5,6],[0,1,2,3,4,5,6,7],[1,2,3,4,5,6,7,0],[2,3,4,5,6,7,0,1],[3,4,5,6,7,0,1,2],[4,5,6,7,0,1,2,3]],"identity":3,"prime":2,"element":7}。請依 [group_order, prime, element, positive_power_rows, p_power_is_identity, no_smaller_positive_identity_power, certificate] 欄序回答。

g^p=e與所有較小正冪不等於e須分開核；identity雖滿足g^p=e，卻不是order-p witness。

查看答案與解釋(8, 2, 7, [[1, 7], [2, 3]], 是, 是, g_to_p_is_identity_and_no_smaller_positive_power_is)

Wave6第六層核對=(8, 2, 7, [[1, 7], [2, 3]], 是, 是, g_to_p_is_identity_and_no_smaller_positive_power_is)；依完整明示資料獨立重算；order-p witness必須同時驗g^p=e與所有1<=k<p皆有g^k!=e；完整有限枚舉只證指定model；composite divisor不保證是某元素的階。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261112-r01-cauchy-theorem-finite-groups-0067/)

有限群的Cauchy定理 · qf-mod43-cauchy-order-p-witness · candidate





## 68. 有限群的Cauchy定理

完整有限群、prime divisor與exact element-order證書。操作=cauchy-order-p-witness；資料={"group_table":[[7,8,9,0,1,2,3,4,5,6],[8,9,0,1,2,3,4,5,6,7],[9,0,1,2,3,4,5,6,7,8],[0,1,2,3,4,5,6,7,8,9],[1,2,3,4,5,6,7,8,9,0],[2,3,4,5,6,7,8,9,0,1],[3,4,5,6,7,8,9,0,1,2],[4,5,6,7,8,9,0,1,2,3],[5,6,7,8,9,0,1,2,3,4],[6,7,8,9,0,1,2,3,4,5]],"identity":3,"prime":2,"element":8}。請依 [group_order, prime, element, positive_power_rows, p_power_is_identity, no_smaller_positive_identity_power, certificate] 欄序回答。

g^p=e與所有較小正冪不等於e須分開核；identity雖滿足g^p=e，卻不是order-p witness。

查看答案與解釋(10, 2, 8, [[1, 8], [2, 3]], 是, 是, g_to_p_is_identity_and_no_smaller_positive_power_is)

Wave6第六層核對=(10, 2, 8, [[1, 8], [2, 3]], 是, 是, g_to_p_is_identity_and_no_smaller_positive_power_is)；依完整明示資料獨立重算；order-p witness必須同時驗g^p=e與所有1<=k<p皆有g^k!=e；完整有限枚舉只證指定model；composite divisor不保證是某元素的階。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261112-r01-cauchy-theorem-finite-groups-0068/)

有限群的Cauchy定理 · qf-mod43-cauchy-order-p-witness · candidate





## 69. 有限群的Cauchy定理

完整有限群、prime divisor與exact element-order證書。操作=cauchy-order-p-witness；資料={"group_table":[[9,10,11,0,1,2,3,4,5,6,7,8],[10,11,0,1,2,3,4,5,6,7,8,9],[11,0,1,2,3,4,5,6,7,8,9,10],[0,1,2,3,4,5,6,7,8,9,10,11],[1,2,3,4,5,6,7,8,9,10,11,0],[2,3,4,5,6,7,8,9,10,11,0,1],[3,4,5,6,7,8,9,10,11,0,1,2],[4,5,6,7,8,9,10,11,0,1,2,3],[5,6,7,8,9,10,11,0,1,2,3,4],[6,7,8,9,10,11,0,1,2,3,4,5],[7,8,9,10,11,0,1,2,3,4,5,6],[8,9,10,11,0,1,2,3,4,5,6,7]],"identity":3,"prime":2,"element":9}。請依 [group_order, prime, element, positive_power_rows, p_power_is_identity, no_smaller_positive_identity_power, certificate] 欄序回答。

g^p=e與所有較小正冪不等於e須分開核；identity雖滿足g^p=e，卻不是order-p witness。

查看答案與解釋(12, 2, 9, [[1, 9], [2, 3]], 是, 是, g_to_p_is_identity_and_no_smaller_positive_power_is)

Wave6第六層核對=(12, 2, 9, [[1, 9], [2, 3]], 是, 是, g_to_p_is_identity_and_no_smaller_positive_power_is)；依完整明示資料獨立重算；order-p witness必須同時驗g^p=e與所有1<=k<p皆有g^k!=e；完整有限枚舉只證指定model；composite divisor不保證是某元素的階。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261112-r01-cauchy-theorem-finite-groups-0069/)

有限群的Cauchy定理 · qf-mod43-cauchy-order-p-witness · candidate





## 70. 有限群的Cauchy定理

完整有限群、prime divisor與exact element-order證書。操作=cauchy-order-p-witness；資料={"group_table":[[11,12,13,0,1,2,3,4,5,6,7,8,9,10],[12,13,0,1,2,3,4,5,6,7,8,9,10,11],[13,0,1,2,3,4,5,6,7,8,9,10,11,12],[0,1,2,3,4,5,6,7,8,9,10,11,12,13],[1,2,3,4,5,6,7,8,9,10,11,12,13,0],[2,3,4,5,6,7,8,9,10,11,12,13,0,1],[3,4,5,6,7,8,9,10,11,12,13,0,1,2],[4,5,6,7,8,9,10,11,12,13,0,1,2,3],[5,6,7,8,9,10,11,12,13,0,1,2,3,4],[6,7,8,9,10,11,12,13,0,1,2,3,4,5],[7,8,9,10,11,12,13,0,1,2,3,4,5,6],[8,9,10,11,12,13,0,1,2,3,4,5,6,7],[9,10,11,12,13,0,1,2,3,4,5,6,7,8],[10,11,12,13,0,1,2,3,4,5,6,7,8,9]],"identity":3,"prime":2,"element":10}。請依 [group_order, prime, element, positive_power_rows, p_power_is_identity, no_smaller_positive_identity_power, certificate] 欄序回答。

g^p=e與所有較小正冪不等於e須分開核；identity雖滿足g^p=e，卻不是order-p witness。

查看答案與解釋(14, 2, 10, [[1, 10], [2, 3]], 是, 是, g_to_p_is_identity_and_no_smaller_positive_power_is)

Wave6第六層核對=(14, 2, 10, [[1, 10], [2, 3]], 是, 是, g_to_p_is_identity_and_no_smaller_positive_power_is)；依完整明示資料獨立重算；order-p witness必須同時驗g^p=e與所有1<=k<p皆有g^k!=e；完整有限枚舉只證指定model；composite divisor不保證是某元素的階。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261112-r01-cauchy-theorem-finite-groups-0070/)

有限群的Cauchy定理 · qf-mod43-cauchy-order-p-witness · candidate





## 71. 有限群的Cauchy定理

完整有限群、prime divisor與exact element-order證書。操作=cauchy-order-p-witness；資料={"group_table":[[2,3,4,5,0,1],[3,4,5,0,1,2],[4,5,0,1,2,3],[5,0,1,2,3,4],[0,1,2,3,4,5],[1,2,3,4,5,0]],"identity":4,"prime":2,"element":1}。請依 [group_order, prime, element, positive_power_rows, p_power_is_identity, no_smaller_positive_identity_power, certificate] 欄序回答。

g^p=e與所有較小正冪不等於e須分開核；identity雖滿足g^p=e，卻不是order-p witness。

查看答案與解釋(6, 2, 1, [[1, 1], [2, 4]], 是, 是, g_to_p_is_identity_and_no_smaller_positive_power_is)

Wave6第六層核對=(6, 2, 1, [[1, 1], [2, 4]], 是, 是, g_to_p_is_identity_and_no_smaller_positive_power_is)；依完整明示資料獨立重算；order-p witness必須同時驗g^p=e與所有1<=k<p皆有g^k!=e；完整有限枚舉只證指定model；composite divisor不保證是某元素的階。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261112-r01-cauchy-theorem-finite-groups-0071/)

有限群的Cauchy定理 · qf-mod43-cauchy-order-p-witness · candidate





## 72. 有限群的Cauchy定理

完整有限群、prime divisor與exact element-order證書。操作=cauchy-order-p-witness；資料={"group_table":[[4,5,6,7,0,1,2,3],[5,6,7,0,1,2,3,4],[6,7,0,1,2,3,4,5],[7,0,1,2,3,4,5,6],[0,1,2,3,4,5,6,7],[1,2,3,4,5,6,7,0],[2,3,4,5,6,7,0,1],[3,4,5,6,7,0,1,2]],"identity":4,"prime":2,"element":0}。請依 [group_order, prime, element, positive_power_rows, p_power_is_identity, no_smaller_positive_identity_power, certificate] 欄序回答。

g^p=e與所有較小正冪不等於e須分開核；identity雖滿足g^p=e，卻不是order-p witness。

查看答案與解釋(8, 2, 0, [[1, 0], [2, 4]], 是, 是, g_to_p_is_identity_and_no_smaller_positive_power_is)

Wave6第六層核對=(8, 2, 0, [[1, 0], [2, 4]], 是, 是, g_to_p_is_identity_and_no_smaller_positive_power_is)；依完整明示資料獨立重算；order-p witness必須同時驗g^p=e與所有1<=k<p皆有g^k!=e；完整有限枚舉只證指定model；composite divisor不保證是某元素的階。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261112-r01-cauchy-theorem-finite-groups-0072/)

有限群的Cauchy定理 · qf-mod43-cauchy-order-p-witness · candidate





## 73. 有限群的Cauchy定理

完整有限群、prime divisor與exact element-order證書。操作=cauchy-order-p-witness；資料={"group_table":[[6,7,8,9,0,1,2,3,4,5],[7,8,9,0,1,2,3,4,5,6],[8,9,0,1,2,3,4,5,6,7],[9,0,1,2,3,4,5,6,7,8],[0,1,2,3,4,5,6,7,8,9],[1,2,3,4,5,6,7,8,9,0],[2,3,4,5,6,7,8,9,0,1],[3,4,5,6,7,8,9,0,1,2],[4,5,6,7,8,9,0,1,2,3],[5,6,7,8,9,0,1,2,3,4]],"identity":4,"prime":2,"element":9}。請依 [group_order, prime, element, positive_power_rows, p_power_is_identity, no_smaller_positive_identity_power, certificate] 欄序回答。

g^p=e與所有較小正冪不等於e須分開核；identity雖滿足g^p=e，卻不是order-p witness。

查看答案與解釋(10, 2, 9, [[1, 9], [2, 4]], 是, 是, g_to_p_is_identity_and_no_smaller_positive_power_is)

Wave6第六層核對=(10, 2, 9, [[1, 9], [2, 4]], 是, 是, g_to_p_is_identity_and_no_smaller_positive_power_is)；依完整明示資料獨立重算；order-p witness必須同時驗g^p=e與所有1<=k<p皆有g^k!=e；完整有限枚舉只證指定model；composite divisor不保證是某元素的階。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261112-r01-cauchy-theorem-finite-groups-0073/)

有限群的Cauchy定理 · qf-mod43-cauchy-order-p-witness · candidate





## 74. 有限群的Cauchy定理

完整有限群、prime divisor與exact element-order證書。操作=cauchy-order-p-witness；資料={"group_table":[[8,9,10,11,0,1,2,3,4,5,6,7],[9,10,11,0,1,2,3,4,5,6,7,8],[10,11,0,1,2,3,4,5,6,7,8,9],[11,0,1,2,3,4,5,6,7,8,9,10],[0,1,2,3,4,5,6,7,8,9,10,11],[1,2,3,4,5,6,7,8,9,10,11,0],[2,3,4,5,6,7,8,9,10,11,0,1],[3,4,5,6,7,8,9,10,11,0,1,2],[4,5,6,7,8,9,10,11,0,1,2,3],[5,6,7,8,9,10,11,0,1,2,3,4],[6,7,8,9,10,11,0,1,2,3,4,5],[7,8,9,10,11,0,1,2,3,4,5,6]],"identity":4,"prime":2,"element":10}。請依 [group_order, prime, element, positive_power_rows, p_power_is_identity, no_smaller_positive_identity_power, certificate] 欄序回答。

g^p=e與所有較小正冪不等於e須分開核；identity雖滿足g^p=e，卻不是order-p witness。

查看答案與解釋(12, 2, 10, [[1, 10], [2, 4]], 是, 是, g_to_p_is_identity_and_no_smaller_positive_power_is)

Wave6第六層核對=(12, 2, 10, [[1, 10], [2, 4]], 是, 是, g_to_p_is_identity_and_no_smaller_positive_power_is)；依完整明示資料獨立重算；order-p witness必須同時驗g^p=e與所有1<=k<p皆有g^k!=e；完整有限枚舉只證指定model；composite divisor不保證是某元素的階。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261112-r01-cauchy-theorem-finite-groups-0074/)

有限群的Cauchy定理 · qf-mod43-cauchy-order-p-witness · candidate





## 75. 有限群的Cauchy定理

完整有限群、prime divisor與exact element-order證書。操作=cauchy-order-p-witness；資料={"group_table":[[10,11,12,13,0,1,2,3,4,5,6,7,8,9],[11,12,13,0,1,2,3,4,5,6,7,8,9,10],[12,13,0,1,2,3,4,5,6,7,8,9,10,11],[13,0,1,2,3,4,5,6,7,8,9,10,11,12],[0,1,2,3,4,5,6,7,8,9,10,11,12,13],[1,2,3,4,5,6,7,8,9,10,11,12,13,0],[2,3,4,5,6,7,8,9,10,11,12,13,0,1],[3,4,5,6,7,8,9,10,11,12,13,0,1,2],[4,5,6,7,8,9,10,11,12,13,0,1,2,3],[5,6,7,8,9,10,11,12,13,0,1,2,3,4],[6,7,8,9,10,11,12,13,0,1,2,3,4,5],[7,8,9,10,11,12,13,0,1,2,3,4,5,6],[8,9,10,11,12,13,0,1,2,3,4,5,6,7],[9,10,11,12,13,0,1,2,3,4,5,6,7,8]],"identity":4,"prime":2,"element":11}。請依 [group_order, prime, element, positive_power_rows, p_power_is_identity, no_smaller_positive_identity_power, certificate] 欄序回答。

g^p=e與所有較小正冪不等於e須分開核；identity雖滿足g^p=e，卻不是order-p witness。

查看答案與解釋(14, 2, 11, [[1, 11], [2, 4]], 是, 是, g_to_p_is_identity_and_no_smaller_positive_power_is)

Wave6第六層核對=(14, 2, 11, [[1, 11], [2, 4]], 是, 是, g_to_p_is_identity_and_no_smaller_positive_power_is)；依完整明示資料獨立重算；order-p witness必須同時驗g^p=e與所有1<=k<p皆有g^k!=e；完整有限枚舉只證指定model；composite divisor不保證是某元素的階。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261112-r01-cauchy-theorem-finite-groups-0075/)

有限群的Cauchy定理 · qf-mod43-cauchy-order-p-witness · candidate





## 76. 有限群的Cauchy定理

完整有限群、prime divisor與exact element-order證書。操作=cauchy-composite-divisor-boundary；資料={"group_table":[[0,1,2,3],[1,0,3,2],[2,3,0,1],[3,2,1,0]],"identity":0,"divisor":4}。請依 [group_order, composite_divisor, element_order_rows, divisor_divides_order, exists_element_of_requested_order, boundary] 欄序回答。

查看答案與解釋(4, 4, [[0, 1], [1, 2], [2, 2], [3, 2]], 是, 否, composite_divisor_need_not_be_an_element_order)

Wave6第六層核對=(4, 4, [[0, 1], [1, 2], [2, 2], [3, 2]], 是, 否, composite_divisor_need_not_be_an_element_order)；依完整明示資料獨立重算；order-p witness必須同時驗g^p=e與所有1<=k<p皆有g^k!=e；完整有限枚舉只證指定model；composite divisor不保證是某元素的階。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261112-r01-cauchy-theorem-finite-groups-0076/)

有限群的Cauchy定理 · qf-mod43-cauchy-composite-divisor-boundary · candidate





## 77. 有限群的Cauchy定理

完整有限群、prime divisor與exact element-order證書。操作=cauchy-composite-divisor-boundary；資料={"group_table":[[1,0,3,2],[0,1,2,3],[3,2,1,0],[2,3,0,1]],"identity":1,"divisor":4}。請依 [group_order, composite_divisor, element_order_rows, divisor_divides_order, exists_element_of_requested_order, boundary] 欄序回答。

查看答案與解釋(4, 4, [[0, 2], [1, 1], [2, 2], [3, 2]], 是, 否, composite_divisor_need_not_be_an_element_order)

Wave6第六層核對=(4, 4, [[0, 2], [1, 1], [2, 2], [3, 2]], 是, 否, composite_divisor_need_not_be_an_element_order)；依完整明示資料獨立重算；order-p witness必須同時驗g^p=e與所有1<=k<p皆有g^k!=e；完整有限枚舉只證指定model；composite divisor不保證是某元素的階。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261112-r01-cauchy-theorem-finite-groups-0077/)

有限群的Cauchy定理 · qf-mod43-cauchy-composite-divisor-boundary · candidate





## 78. 有限群的Cauchy定理

完整有限群、prime divisor與exact element-order證書。操作=cauchy-composite-divisor-boundary；資料={"group_table":[[2,3,0,1],[3,2,1,0],[0,1,2,3],[1,0,3,2]],"identity":2,"divisor":4}。請依 [group_order, composite_divisor, element_order_rows, divisor_divides_order, exists_element_of_requested_order, boundary] 欄序回答。

查看答案與解釋(4, 4, [[0, 2], [1, 2], [2, 1], [3, 2]], 是, 否, composite_divisor_need_not_be_an_element_order)

Wave6第六層核對=(4, 4, [[0, 2], [1, 2], [2, 1], [3, 2]], 是, 否, composite_divisor_need_not_be_an_element_order)；依完整明示資料獨立重算；order-p witness必須同時驗g^p=e與所有1<=k<p皆有g^k!=e；完整有限枚舉只證指定model；composite divisor不保證是某元素的階。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261112-r01-cauchy-theorem-finite-groups-0078/)

有限群的Cauchy定理 · qf-mod43-cauchy-composite-divisor-boundary · candidate





## 79. 有限群的Cauchy定理

完整有限群、prime divisor與exact element-order證書。操作=cauchy-composite-divisor-boundary；資料={"group_table":[[3,2,1,0],[2,3,0,1],[1,0,3,2],[0,1,2,3]],"identity":3,"divisor":4}。請依 [group_order, composite_divisor, element_order_rows, divisor_divides_order, exists_element_of_requested_order, boundary] 欄序回答。

查看答案與解釋(4, 4, [[0, 2], [1, 2], [2, 2], [3, 1]], 是, 否, composite_divisor_need_not_be_an_element_order)

Wave6第六層核對=(4, 4, [[0, 2], [1, 2], [2, 2], [3, 1]], 是, 否, composite_divisor_need_not_be_an_element_order)；依完整明示資料獨立重算；order-p witness必須同時驗g^p=e與所有1<=k<p皆有g^k!=e；完整有限枚舉只證指定model；composite divisor不保證是某元素的階。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261112-r01-cauchy-theorem-finite-groups-0079/)

有限群的Cauchy定理 · qf-mod43-cauchy-composite-divisor-boundary · candidate





## 80. 有限群的Cauchy定理

完整有限群、prime divisor與exact element-order證書。操作=cauchy-composite-divisor-boundary；資料={"group_table":[[0,1,2,3,4,5,6,7],[1,0,3,2,5,4,7,6],[2,3,0,1,6,7,4,5],[3,2,1,0,7,6,5,4],[4,5,6,7,0,1,2,3],[5,4,7,6,1,0,3,2],[6,7,4,5,2,3,0,1],[7,6,5,4,3,2,1,0]],"identity":0,"divisor":8}。請依 [group_order, composite_divisor, element_order_rows, divisor_divides_order, exists_element_of_requested_order, boundary] 欄序回答。

查看答案與解釋(8, 8, [[0, 1], [1, 2], [2, 2], [3, 2], [4, 2], [5, 2], [6, 2], [7, 2]], 是, 否, composite_divisor_need_not_be_an_element_order)

Wave6第六層核對=(8, 8, [[0, 1], [1, 2], [2, 2], [3, 2], [4, 2], [5, 2], [6, 2], [7, 2]], 是, 否, composite_divisor_need_not_be_an_element_order)；依完整明示資料獨立重算；order-p witness必須同時驗g^p=e與所有1<=k<p皆有g^k!=e；完整有限枚舉只證指定model；composite divisor不保證是某元素的階。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261112-r01-cauchy-theorem-finite-groups-0080/)

有限群的Cauchy定理 · qf-mod43-cauchy-composite-divisor-boundary · candidate





## 81. 有限群的Cauchy定理

完整有限群、prime divisor與exact element-order證書。操作=cauchy-composite-divisor-boundary；資料={"group_table":[[1,0,3,2,5,4,7,6],[0,1,2,3,4,5,6,7],[3,2,1,0,7,6,5,4],[2,3,0,1,6,7,4,5],[5,4,7,6,1,0,3,2],[4,5,6,7,0,1,2,3],[7,6,5,4,3,2,1,0],[6,7,4,5,2,3,0,1]],"identity":1,"divisor":8}。請依 [group_order, composite_divisor, element_order_rows, divisor_divides_order, exists_element_of_requested_order, boundary] 欄序回答。

查看答案與解釋(8, 8, [[0, 2], [1, 1], [2, 2], [3, 2], [4, 2], [5, 2], [6, 2], [7, 2]], 是, 否, composite_divisor_need_not_be_an_element_order)

Wave6第六層核對=(8, 8, [[0, 2], [1, 1], [2, 2], [3, 2], [4, 2], [5, 2], [6, 2], [7, 2]], 是, 否, composite_divisor_need_not_be_an_element_order)；依完整明示資料獨立重算；order-p witness必須同時驗g^p=e與所有1<=k<p皆有g^k!=e；完整有限枚舉只證指定model；composite divisor不保證是某元素的階。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261112-r01-cauchy-theorem-finite-groups-0081/)

有限群的Cauchy定理 · qf-mod43-cauchy-composite-divisor-boundary · candidate





## 82. 有限群的Cauchy定理

完整有限群、prime divisor與exact element-order證書。操作=cauchy-composite-divisor-boundary；資料={"group_table":[[2,3,0,1,6,7,4,5],[3,2,1,0,7,6,5,4],[0,1,2,3,4,5,6,7],[1,0,3,2,5,4,7,6],[6,7,4,5,2,3,0,1],[7,6,5,4,3,2,1,0],[4,5,6,7,0,1,2,3],[5,4,7,6,1,0,3,2]],"identity":2,"divisor":8}。請依 [group_order, composite_divisor, element_order_rows, divisor_divides_order, exists_element_of_requested_order, boundary] 欄序回答。

查看答案與解釋(8, 8, [[0, 2], [1, 2], [2, 1], [3, 2], [4, 2], [5, 2], [6, 2], [7, 2]], 是, 否, composite_divisor_need_not_be_an_element_order)

Wave6第六層核對=(8, 8, [[0, 2], [1, 2], [2, 1], [3, 2], [4, 2], [5, 2], [6, 2], [7, 2]], 是, 否, composite_divisor_need_not_be_an_element_order)；依完整明示資料獨立重算；order-p witness必須同時驗g^p=e與所有1<=k<p皆有g^k!=e；完整有限枚舉只證指定model；composite divisor不保證是某元素的階。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261112-r01-cauchy-theorem-finite-groups-0082/)

有限群的Cauchy定理 · qf-mod43-cauchy-composite-divisor-boundary · candidate





## 83. 有限群的Cauchy定理

完整有限群、prime divisor與exact element-order證書。操作=cauchy-composite-divisor-boundary；資料={"group_table":[[3,2,1,0,7,6,5,4],[2,3,0,1,6,7,4,5],[1,0,3,2,5,4,7,6],[0,1,2,3,4,5,6,7],[7,6,5,4,3,2,1,0],[6,7,4,5,2,3,0,1],[5,4,7,6,1,0,3,2],[4,5,6,7,0,1,2,3]],"identity":3,"divisor":8}。請依 [group_order, composite_divisor, element_order_rows, divisor_divides_order, exists_element_of_requested_order, boundary] 欄序回答。

查看答案與解釋(8, 8, [[0, 2], [1, 2], [2, 2], [3, 1], [4, 2], [5, 2], [6, 2], [7, 2]], 是, 否, composite_divisor_need_not_be_an_element_order)

Wave6第六層核對=(8, 8, [[0, 2], [1, 2], [2, 2], [3, 1], [4, 2], [5, 2], [6, 2], [7, 2]], 是, 否, composite_divisor_need_not_be_an_element_order)；依完整明示資料獨立重算；order-p witness必須同時驗g^p=e與所有1<=k<p皆有g^k!=e；完整有限枚舉只證指定model；composite divisor不保證是某元素的階。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261112-r01-cauchy-theorem-finite-groups-0083/)

有限群的Cauchy定理 · qf-mod43-cauchy-composite-divisor-boundary · candidate





## 84. 有限群的Cauchy定理

完整有限群、prime divisor與exact element-order證書。操作=cauchy-composite-divisor-boundary；資料={"group_table":[[4,5,6,7,0,1,2,3],[5,4,7,6,1,0,3,2],[6,7,4,5,2,3,0,1],[7,6,5,4,3,2,1,0],[0,1,2,3,4,5,6,7],[1,0,3,2,5,4,7,6],[2,3,0,1,6,7,4,5],[3,2,1,0,7,6,5,4]],"identity":4,"divisor":8}。請依 [group_order, composite_divisor, element_order_rows, divisor_divides_order, exists_element_of_requested_order, boundary] 欄序回答。

查看答案與解釋(8, 8, [[0, 2], [1, 2], [2, 2], [3, 2], [4, 1], [5, 2], [6, 2], [7, 2]], 是, 否, composite_divisor_need_not_be_an_element_order)

Wave6第六層核對=(8, 8, [[0, 2], [1, 2], [2, 2], [3, 2], [4, 1], [5, 2], [6, 2], [7, 2]], 是, 否, composite_divisor_need_not_be_an_element_order)；依完整明示資料獨立重算；order-p witness必須同時驗g^p=e與所有1<=k<p皆有g^k!=e；完整有限枚舉只證指定model；composite divisor不保證是某元素的階。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261112-r01-cauchy-theorem-finite-groups-0084/)

有限群的Cauchy定理 · qf-mod43-cauchy-composite-divisor-boundary · candidate





## 85. 有限群的Cauchy定理

完整有限群、prime divisor與exact element-order證書。操作=cauchy-composite-divisor-boundary；資料={"group_table":[[5,4,7,6,1,0,3,2],[4,5,6,7,0,1,2,3],[7,6,5,4,3,2,1,0],[6,7,4,5,2,3,0,1],[1,0,3,2,5,4,7,6],[0,1,2,3,4,5,6,7],[3,2,1,0,7,6,5,4],[2,3,0,1,6,7,4,5]],"identity":5,"divisor":8}。請依 [group_order, composite_divisor, element_order_rows, divisor_divides_order, exists_element_of_requested_order, boundary] 欄序回答。

查看答案與解釋(8, 8, [[0, 2], [1, 2], [2, 2], [3, 2], [4, 2], [5, 1], [6, 2], [7, 2]], 是, 否, composite_divisor_need_not_be_an_element_order)

Wave6第六層核對=(8, 8, [[0, 2], [1, 2], [2, 2], [3, 2], [4, 2], [5, 1], [6, 2], [7, 2]], 是, 否, composite_divisor_need_not_be_an_element_order)；依完整明示資料獨立重算；order-p witness必須同時驗g^p=e與所有1<=k<p皆有g^k!=e；完整有限枚舉只證指定model；composite divisor不保證是某元素的階。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261112-r01-cauchy-theorem-finite-groups-0085/)

有限群的Cauchy定理 · qf-mod43-cauchy-composite-divisor-boundary · candidate





## 86. 有限群的Cauchy定理

完整有限群、prime divisor與exact element-order證書。操作=cauchy-composite-divisor-boundary；資料={"group_table":[[6,7,4,5,2,3,0,1],[7,6,5,4,3,2,1,0],[4,5,6,7,0,1,2,3],[5,4,7,6,1,0,3,2],[2,3,0,1,6,7,4,5],[3,2,1,0,7,6,5,4],[0,1,2,3,4,5,6,7],[1,0,3,2,5,4,7,6]],"identity":6,"divisor":8}。請依 [group_order, composite_divisor, element_order_rows, divisor_divides_order, exists_element_of_requested_order, boundary] 欄序回答。

查看答案與解釋(8, 8, [[0, 2], [1, 2], [2, 2], [3, 2], [4, 2], [5, 2], [6, 1], [7, 2]], 是, 否, composite_divisor_need_not_be_an_element_order)

Wave6第六層核對=(8, 8, [[0, 2], [1, 2], [2, 2], [3, 2], [4, 2], [5, 2], [6, 1], [7, 2]], 是, 否, composite_divisor_need_not_be_an_element_order)；依完整明示資料獨立重算；order-p witness必須同時驗g^p=e與所有1<=k<p皆有g^k!=e；完整有限枚舉只證指定model；composite divisor不保證是某元素的階。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261112-r01-cauchy-theorem-finite-groups-0086/)

有限群的Cauchy定理 · qf-mod43-cauchy-composite-divisor-boundary · candidate





## 87. 有限群的Cauchy定理

完整有限群、prime divisor與exact element-order證書。操作=cauchy-composite-divisor-boundary；資料={"group_table":[[7,6,5,4,3,2,1,0],[6,7,4,5,2,3,0,1],[5,4,7,6,1,0,3,2],[4,5,6,7,0,1,2,3],[3,2,1,0,7,6,5,4],[2,3,0,1,6,7,4,5],[1,0,3,2,5,4,7,6],[0,1,2,3,4,5,6,7]],"identity":7,"divisor":8}。請依 [group_order, composite_divisor, element_order_rows, divisor_divides_order, exists_element_of_requested_order, boundary] 欄序回答。

查看答案與解釋(8, 8, [[0, 2], [1, 2], [2, 2], [3, 2], [4, 2], [5, 2], [6, 2], [7, 1]], 是, 否, composite_divisor_need_not_be_an_element_order)

Wave6第六層核對=(8, 8, [[0, 2], [1, 2], [2, 2], [3, 2], [4, 2], [5, 2], [6, 2], [7, 1]], 是, 否, composite_divisor_need_not_be_an_element_order)；依完整明示資料獨立重算；order-p witness必須同時驗g^p=e與所有1<=k<p皆有g^k!=e；完整有限枚舉只證指定model；composite divisor不保證是某元素的階。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261112-r01-cauchy-theorem-finite-groups-0087/)

有限群的Cauchy定理 · qf-mod43-cauchy-composite-divisor-boundary · candidate





## 88. 有限群的Cauchy定理

完整有限群、prime divisor與exact element-order證書。操作=cauchy-composite-divisor-boundary；資料={"group_table":[[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15],[1,0,3,2,5,4,7,6,9,8,11,10,13,12,15,14],[2,3,0,1,6,7,4,5,10,11,8,9,14,15,12,13],[3,2,1,0,7,6,5,4,11,10,9,8,15,14,13,12],[4,5,6,7,0,1,2,3,12,13,14,15,8,9,10,11],[5,4,7,6,1,0,3,2,13,12,15,14,9,8,11,10],[6,7,4,5,2,3,0,1,14,15,12,13,10,11,8,9],[7,6,5,4,3,2,1,0,15,14,13,12,11,10,9,8],[8,9,10,11,12,13,14,15,0,1,2,3,4,5,6,7],[9,8,11,10,13,12,15,14,1,0,3,2,5,4,7,6],[10,11,8,9,14,15,12,13,2,3,0,1,6,7,4,5],[11,10,9,8,15,14,13,12,3,2,1,0,7,6,5,4],[12,13,14,15,8,9,10,11,4,5,6,7,0,1,2,3],[13,12,15,14,9,8,11,10,5,4,7,6,1,0,3,2],[14,15,12,13,10,11,8,9,6,7,4,5,2,3,0,1],[15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0]],"identity":0,"divisor":16}。請依 [group_order, composite_divisor, element_order_rows, divisor_divides_order, exists_element_of_requested_order, boundary] 欄序回答。

查看答案與解釋(16, 16, [[0, 1], [1, 2], [2, 2], [3, 2], [4, 2], [5, 2], [6, 2], [7, 2], [8, 2], [9, 2], [10, 2], [11, 2], [12, 2], [13, 2], [14, 2], [15, 2]], 是, 否, composite_divisor_need_not_be_an_element_order)

Wave6第六層核對=(16, 16, [[0, 1], [1, 2], [2, 2], [3, 2], [4, 2], [5, 2], [6, 2], [7, 2], [8, 2], [9, 2], [10, 2], [11, 2], [12, 2], [13, 2], [14, 2], [15, 2]], 是, 否, composite_divisor_need_not_be_an_element_order)；依完整明示資料獨立重算；order-p witness必須同時驗g^p=e與所有1<=k<p皆有g^k!=e；完整有限枚舉只證指定model；composite divisor不保證是某元素的階。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261112-r01-cauchy-theorem-finite-groups-0088/)

有限群的Cauchy定理 · qf-mod43-cauchy-composite-divisor-boundary · candidate





## 89. 有限群的Cauchy定理

完整有限群、prime divisor與exact element-order證書。操作=cauchy-composite-divisor-boundary；資料={"group_table":[[1,0,3,2,5,4,7,6,9,8,11,10,13,12,15,14],[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15],[3,2,1,0,7,6,5,4,11,10,9,8,15,14,13,12],[2,3,0,1,6,7,4,5,10,11,8,9,14,15,12,13],[5,4,7,6,1,0,3,2,13,12,15,14,9,8,11,10],[4,5,6,7,0,1,2,3,12,13,14,15,8,9,10,11],[7,6,5,4,3,2,1,0,15,14,13,12,11,10,9,8],[6,7,4,5,2,3,0,1,14,15,12,13,10,11,8,9],[9,8,11,10,13,12,15,14,1,0,3,2,5,4,7,6],[8,9,10,11,12,13,14,15,0,1,2,3,4,5,6,7],[11,10,9,8,15,14,13,12,3,2,1,0,7,6,5,4],[10,11,8,9,14,15,12,13,2,3,0,1,6,7,4,5],[13,12,15,14,9,8,11,10,5,4,7,6,1,0,3,2],[12,13,14,15,8,9,10,11,4,5,6,7,0,1,2,3],[15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0],[14,15,12,13,10,11,8,9,6,7,4,5,2,3,0,1]],"identity":1,"divisor":16}。請依 [group_order, composite_divisor, element_order_rows, divisor_divides_order, exists_element_of_requested_order, boundary] 欄序回答。

查看答案與解釋(16, 16, [[0, 2], [1, 1], [2, 2], [3, 2], [4, 2], [5, 2], [6, 2], [7, 2], [8, 2], [9, 2], [10, 2], [11, 2], [12, 2], [13, 2], [14, 2], [15, 2]], 是, 否, composite_divisor_need_not_be_an_element_order)

Wave6第六層核對=(16, 16, [[0, 2], [1, 1], [2, 2], [3, 2], [4, 2], [5, 2], [6, 2], [7, 2], [8, 2], [9, 2], [10, 2], [11, 2], [12, 2], [13, 2], [14, 2], [15, 2]], 是, 否, composite_divisor_need_not_be_an_element_order)；依完整明示資料獨立重算；order-p witness必須同時驗g^p=e與所有1<=k<p皆有g^k!=e；完整有限枚舉只證指定model；composite divisor不保證是某元素的階。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261112-r01-cauchy-theorem-finite-groups-0089/)

有限群的Cauchy定理 · qf-mod43-cauchy-composite-divisor-boundary · candidate





## 90. 有限群的Cauchy定理

完整有限群、prime divisor與exact element-order證書。操作=cauchy-composite-divisor-boundary；資料={"group_table":[[2,3,0,1,6,7,4,5,10,11,8,9,14,15,12,13],[3,2,1,0,7,6,5,4,11,10,9,8,15,14,13,12],[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15],[1,0,3,2,5,4,7,6,9,8,11,10,13,12,15,14],[6,7,4,5,2,3,0,1,14,15,12,13,10,11,8,9],[7,6,5,4,3,2,1,0,15,14,13,12,11,10,9,8],[4,5,6,7,0,1,2,3,12,13,14,15,8,9,10,11],[5,4,7,6,1,0,3,2,13,12,15,14,9,8,11,10],[10,11,8,9,14,15,12,13,2,3,0,1,6,7,4,5],[11,10,9,8,15,14,13,12,3,2,1,0,7,6,5,4],[8,9,10,11,12,13,14,15,0,1,2,3,4,5,6,7],[9,8,11,10,13,12,15,14,1,0,3,2,5,4,7,6],[14,15,12,13,10,11,8,9,6,7,4,5,2,3,0,1],[15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0],[12,13,14,15,8,9,10,11,4,5,6,7,0,1,2,3],[13,12,15,14,9,8,11,10,5,4,7,6,1,0,3,2]],"identity":2,"divisor":16}。請依 [group_order, composite_divisor, element_order_rows, divisor_divides_order, exists_element_of_requested_order, boundary] 欄序回答。

查看答案與解釋(16, 16, [[0, 2], [1, 2], [2, 1], [3, 2], [4, 2], [5, 2], [6, 2], [7, 2], [8, 2], [9, 2], [10, 2], [11, 2], [12, 2], [13, 2], [14, 2], [15, 2]], 是, 否, composite_divisor_need_not_be_an_element_order)

Wave6第六層核對=(16, 16, [[0, 2], [1, 2], [2, 1], [3, 2], [4, 2], [5, 2], [6, 2], [7, 2], [8, 2], [9, 2], [10, 2], [11, 2], [12, 2], [13, 2], [14, 2], [15, 2]], 是, 否, composite_divisor_need_not_be_an_element_order)；依完整明示資料獨立重算；order-p witness必須同時驗g^p=e與所有1<=k<p皆有g^k!=e；完整有限枚舉只證指定model；composite divisor不保證是某元素的階。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261112-r01-cauchy-theorem-finite-groups-0090/)

有限群的Cauchy定理 · qf-mod43-cauchy-composite-divisor-boundary · candidate





## 91. 有限群的Cauchy定理

完整有限群、prime divisor與exact element-order證書。操作=cauchy-composite-divisor-boundary；資料={"group_table":[[3,2,1,0,7,6,5,4,11,10,9,8,15,14,13,12],[2,3,0,1,6,7,4,5,10,11,8,9,14,15,12,13],[1,0,3,2,5,4,7,6,9,8,11,10,13,12,15,14],[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15],[7,6,5,4,3,2,1,0,15,14,13,12,11,10,9,8],[6,7,4,5,2,3,0,1,14,15,12,13,10,11,8,9],[5,4,7,6,1,0,3,2,13,12,15,14,9,8,11,10],[4,5,6,7,0,1,2,3,12,13,14,15,8,9,10,11],[11,10,9,8,15,14,13,12,3,2,1,0,7,6,5,4],[10,11,8,9,14,15,12,13,2,3,0,1,6,7,4,5],[9,8,11,10,13,12,15,14,1,0,3,2,5,4,7,6],[8,9,10,11,12,13,14,15,0,1,2,3,4,5,6,7],[15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0],[14,15,12,13,10,11,8,9,6,7,4,5,2,3,0,1],[13,12,15,14,9,8,11,10,5,4,7,6,1,0,3,2],[12,13,14,15,8,9,10,11,4,5,6,7,0,1,2,3]],"identity":3,"divisor":16}。請依 [group_order, composite_divisor, element_order_rows, divisor_divides_order, exists_element_of_requested_order, boundary] 欄序回答。

查看答案與解釋(16, 16, [[0, 2], [1, 2], [2, 2], [3, 1], [4, 2], [5, 2], [6, 2], [7, 2], [8, 2], [9, 2], [10, 2], [11, 2], [12, 2], [13, 2], [14, 2], [15, 2]], 是, 否, composite_divisor_need_not_be_an_element_order)

Wave6第六層核對=(16, 16, [[0, 2], [1, 2], [2, 2], [3, 1], [4, 2], [5, 2], [6, 2], [7, 2], [8, 2], [9, 2], [10, 2], [11, 2], [12, 2], [13, 2], [14, 2], [15, 2]], 是, 否, composite_divisor_need_not_be_an_element_order)；依完整明示資料獨立重算；order-p witness必須同時驗g^p=e與所有1<=k<p皆有g^k!=e；完整有限枚舉只證指定model；composite divisor不保證是某元素的階。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261112-r01-cauchy-theorem-finite-groups-0091/)

有限群的Cauchy定理 · qf-mod43-cauchy-composite-divisor-boundary · candidate





## 92. 有限群的Cauchy定理

完整有限群、prime divisor與exact element-order證書。操作=cauchy-composite-divisor-boundary；資料={"group_table":[[4,5,6,7,0,1,2,3,12,13,14,15,8,9,10,11],[5,4,7,6,1,0,3,2,13,12,15,14,9,8,11,10],[6,7,4,5,2,3,0,1,14,15,12,13,10,11,8,9],[7,6,5,4,3,2,1,0,15,14,13,12,11,10,9,8],[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15],[1,0,3,2,5,4,7,6,9,8,11,10,13,12,15,14],[2,3,0,1,6,7,4,5,10,11,8,9,14,15,12,13],[3,2,1,0,7,6,5,4,11,10,9,8,15,14,13,12],[12,13,14,15,8,9,10,11,4,5,6,7,0,1,2,3],[13,12,15,14,9,8,11,10,5,4,7,6,1,0,3,2],[14,15,12,13,10,11,8,9,6,7,4,5,2,3,0,1],[15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0],[8,9,10,11,12,13,14,15,0,1,2,3,4,5,6,7],[9,8,11,10,13,12,15,14,1,0,3,2,5,4,7,6],[10,11,8,9,14,15,12,13,2,3,0,1,6,7,4,5],[11,10,9,8,15,14,13,12,3,2,1,0,7,6,5,4]],"identity":4,"divisor":16}。請依 [group_order, composite_divisor, element_order_rows, divisor_divides_order, exists_element_of_requested_order, boundary] 欄序回答。

查看答案與解釋(16, 16, [[0, 2], [1, 2], [2, 2], [3, 2], [4, 1], [5, 2], [6, 2], [7, 2], [8, 2], [9, 2], [10, 2], [11, 2], [12, 2], [13, 2], [14, 2], [15, 2]], 是, 否, composite_divisor_need_not_be_an_element_order)

Wave6第六層核對=(16, 16, [[0, 2], [1, 2], [2, 2], [3, 2], [4, 1], [5, 2], [6, 2], [7, 2], [8, 2], [9, 2], [10, 2], [11, 2], [12, 2], [13, 2], [14, 2], [15, 2]], 是, 否, composite_divisor_need_not_be_an_element_order)；依完整明示資料獨立重算；order-p witness必須同時驗g^p=e與所有1<=k<p皆有g^k!=e；完整有限枚舉只證指定model；composite divisor不保證是某元素的階。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261112-r01-cauchy-theorem-finite-groups-0092/)

有限群的Cauchy定理 · qf-mod43-cauchy-composite-divisor-boundary · candidate





## 93. 有限群的Cauchy定理

完整有限群、prime divisor與exact element-order證書。操作=cauchy-composite-divisor-boundary；資料={"group_table":[[5,4,7,6,1,0,3,2,13,12,15,14,9,8,11,10],[4,5,6,7,0,1,2,3,12,13,14,15,8,9,10,11],[7,6,5,4,3,2,1,0,15,14,13,12,11,10,9,8],[6,7,4,5,2,3,0,1,14,15,12,13,10,11,8,9],[1,0,3,2,5,4,7,6,9,8,11,10,13,12,15,14],[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15],[3,2,1,0,7,6,5,4,11,10,9,8,15,14,13,12],[2,3,0,1,6,7,4,5,10,11,8,9,14,15,12,13],[13,12,15,14,9,8,11,10,5,4,7,6,1,0,3,2],[12,13,14,15,8,9,10,11,4,5,6,7,0,1,2,3],[15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0],[14,15,12,13,10,11,8,9,6,7,4,5,2,3,0,1],[9,8,11,10,13,12,15,14,1,0,3,2,5,4,7,6],[8,9,10,11,12,13,14,15,0,1,2,3,4,5,6,7],[11,10,9,8,15,14,13,12,3,2,1,0,7,6,5,4],[10,11,8,9,14,15,12,13,2,3,0,1,6,7,4,5]],"identity":5,"divisor":16}。請依 [group_order, composite_divisor, element_order_rows, divisor_divides_order, exists_element_of_requested_order, boundary] 欄序回答。

查看答案與解釋(16, 16, [[0, 2], [1, 2], [2, 2], [3, 2], [4, 2], [5, 1], [6, 2], [7, 2], [8, 2], [9, 2], [10, 2], [11, 2], [12, 2], [13, 2], [14, 2], [15, 2]], 是, 否, composite_divisor_need_not_be_an_element_order)

Wave6第六層核對=(16, 16, [[0, 2], [1, 2], [2, 2], [3, 2], [4, 2], [5, 1], [6, 2], [7, 2], [8, 2], [9, 2], [10, 2], [11, 2], [12, 2], [13, 2], [14, 2], [15, 2]], 是, 否, composite_divisor_need_not_be_an_element_order)；依完整明示資料獨立重算；order-p witness必須同時驗g^p=e與所有1<=k<p皆有g^k!=e；完整有限枚舉只證指定model；composite divisor不保證是某元素的階。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261112-r01-cauchy-theorem-finite-groups-0093/)

有限群的Cauchy定理 · qf-mod43-cauchy-composite-divisor-boundary · candidate





## 94. 有限群的Cauchy定理

完整有限群、prime divisor與exact element-order證書。操作=cauchy-composite-divisor-boundary；資料={"group_table":[[6,7,4,5,2,3,0,1,14,15,12,13,10,11,8,9],[7,6,5,4,3,2,1,0,15,14,13,12,11,10,9,8],[4,5,6,7,0,1,2,3,12,13,14,15,8,9,10,11],[5,4,7,6,1,0,3,2,13,12,15,14,9,8,11,10],[2,3,0,1,6,7,4,5,10,11,8,9,14,15,12,13],[3,2,1,0,7,6,5,4,11,10,9,8,15,14,13,12],[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15],[1,0,3,2,5,4,7,6,9,8,11,10,13,12,15,14],[14,15,12,13,10,11,8,9,6,7,4,5,2,3,0,1],[15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0],[12,13,14,15,8,9,10,11,4,5,6,7,0,1,2,3],[13,12,15,14,9,8,11,10,5,4,7,6,1,0,3,2],[10,11,8,9,14,15,12,13,2,3,0,1,6,7,4,5],[11,10,9,8,15,14,13,12,3,2,1,0,7,6,5,4],[8,9,10,11,12,13,14,15,0,1,2,3,4,5,6,7],[9,8,11,10,13,12,15,14,1,0,3,2,5,4,7,6]],"identity":6,"divisor":16}。請依 [group_order, composite_divisor, element_order_rows, divisor_divides_order, exists_element_of_requested_order, boundary] 欄序回答。

查看答案與解釋(16, 16, [[0, 2], [1, 2], [2, 2], [3, 2], [4, 2], [5, 2], [6, 1], [7, 2], [8, 2], [9, 2], [10, 2], [11, 2], [12, 2], [13, 2], [14, 2], [15, 2]], 是, 否, composite_divisor_need_not_be_an_element_order)

Wave6第六層核對=(16, 16, [[0, 2], [1, 2], [2, 2], [3, 2], [4, 2], [5, 2], [6, 1], [7, 2], [8, 2], [9, 2], [10, 2], [11, 2], [12, 2], [13, 2], [14, 2], [15, 2]], 是, 否, composite_divisor_need_not_be_an_element_order)；依完整明示資料獨立重算；order-p witness必須同時驗g^p=e與所有1<=k<p皆有g^k!=e；完整有限枚舉只證指定model；composite divisor不保證是某元素的階。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261112-r01-cauchy-theorem-finite-groups-0094/)

有限群的Cauchy定理 · qf-mod43-cauchy-composite-divisor-boundary · candidate





## 95. 有限群的Cauchy定理

完整有限群、prime divisor與exact element-order證書。操作=cauchy-composite-divisor-boundary；資料={"group_table":[[7,6,5,4,3,2,1,0,15,14,13,12,11,10,9,8],[6,7,4,5,2,3,0,1,14,15,12,13,10,11,8,9],[5,4,7,6,1,0,3,2,13,12,15,14,9,8,11,10],[4,5,6,7,0,1,2,3,12,13,14,15,8,9,10,11],[3,2,1,0,7,6,5,4,11,10,9,8,15,14,13,12],[2,3,0,1,6,7,4,5,10,11,8,9,14,15,12,13],[1,0,3,2,5,4,7,6,9,8,11,10,13,12,15,14],[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15],[15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0],[14,15,12,13,10,11,8,9,6,7,4,5,2,3,0,1],[13,12,15,14,9,8,11,10,5,4,7,6,1,0,3,2],[12,13,14,15,8,9,10,11,4,5,6,7,0,1,2,3],[11,10,9,8,15,14,13,12,3,2,1,0,7,6,5,4],[10,11,8,9,14,15,12,13,2,3,0,1,6,7,4,5],[9,8,11,10,13,12,15,14,1,0,3,2,5,4,7,6],[8,9,10,11,12,13,14,15,0,1,2,3,4,5,6,7]],"identity":7,"divisor":16}。請依 [group_order, composite_divisor, element_order_rows, divisor_divides_order, exists_element_of_requested_order, boundary] 欄序回答。

查看答案與解釋(16, 16, [[0, 2], [1, 2], [2, 2], [3, 2], [4, 2], [5, 2], [6, 2], [7, 1], [8, 2], [9, 2], [10, 2], [11, 2], [12, 2], [13, 2], [14, 2], [15, 2]], 是, 否, composite_divisor_need_not_be_an_element_order)

Wave6第六層核對=(16, 16, [[0, 2], [1, 2], [2, 2], [3, 2], [4, 2], [5, 2], [6, 2], [7, 1], [8, 2], [9, 2], [10, 2], [11, 2], [12, 2], [13, 2], [14, 2], [15, 2]], 是, 否, composite_divisor_need_not_be_an_element_order)；依完整明示資料獨立重算；order-p witness必須同時驗g^p=e與所有1<=k<p皆有g^k!=e；完整有限枚舉只證指定model；composite divisor不保證是某元素的階。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261112-r01-cauchy-theorem-finite-groups-0095/)

有限群的Cauchy定理 · qf-mod43-cauchy-composite-divisor-boundary · candidate





## 96. 有限群的Cauchy定理

完整有限群、prime divisor與exact element-order證書。操作=cauchy-composite-divisor-boundary；資料={"group_table":[[8,9,10,11,12,13,14,15,0,1,2,3,4,5,6,7],[9,8,11,10,13,12,15,14,1,0,3,2,5,4,7,6],[10,11,8,9,14,15,12,13,2,3,0,1,6,7,4,5],[11,10,9,8,15,14,13,12,3,2,1,0,7,6,5,4],[12,13,14,15,8,9,10,11,4,5,6,7,0,1,2,3],[13,12,15,14,9,8,11,10,5,4,7,6,1,0,3,2],[14,15,12,13,10,11,8,9,6,7,4,5,2,3,0,1],[15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0],[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15],[1,0,3,2,5,4,7,6,9,8,11,10,13,12,15,14],[2,3,0,1,6,7,4,5,10,11,8,9,14,15,12,13],[3,2,1,0,7,6,5,4,11,10,9,8,15,14,13,12],[4,5,6,7,0,1,2,3,12,13,14,15,8,9,10,11],[5,4,7,6,1,0,3,2,13,12,15,14,9,8,11,10],[6,7,4,5,2,3,0,1,14,15,12,13,10,11,8,9],[7,6,5,4,3,2,1,0,15,14,13,12,11,10,9,8]],"identity":8,"divisor":16}。請依 [group_order, composite_divisor, element_order_rows, divisor_divides_order, exists_element_of_requested_order, boundary] 欄序回答。

查看答案與解釋(16, 16, [[0, 2], [1, 2], [2, 2], [3, 2], [4, 2], [5, 2], [6, 2], [7, 2], [8, 1], [9, 2], [10, 2], [11, 2], [12, 2], [13, 2], [14, 2], [15, 2]], 是, 否, composite_divisor_need_not_be_an_element_order)

Wave6第六層核對=(16, 16, [[0, 2], [1, 2], [2, 2], [3, 2], [4, 2], [5, 2], [6, 2], [7, 2], [8, 1], [9, 2], [10, 2], [11, 2], [12, 2], [13, 2], [14, 2], [15, 2]], 是, 否, composite_divisor_need_not_be_an_element_order)；依完整明示資料獨立重算；order-p witness必須同時驗g^p=e與所有1<=k<p皆有g^k!=e；完整有限枚舉只證指定model；composite divisor不保證是某元素的階。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261112-r01-cauchy-theorem-finite-groups-0096/)

有限群的Cauchy定理 · qf-mod43-cauchy-composite-divisor-boundary · candidate





## 97. 有限群的Cauchy定理

完整有限群、prime divisor與exact element-order證書。操作=cauchy-composite-divisor-boundary；資料={"group_table":[[9,8,11,10,13,12,15,14,1,0,3,2,5,4,7,6],[8,9,10,11,12,13,14,15,0,1,2,3,4,5,6,7],[11,10,9,8,15,14,13,12,3,2,1,0,7,6,5,4],[10,11,8,9,14,15,12,13,2,3,0,1,6,7,4,5],[13,12,15,14,9,8,11,10,5,4,7,6,1,0,3,2],[12,13,14,15,8,9,10,11,4,5,6,7,0,1,2,3],[15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0],[14,15,12,13,10,11,8,9,6,7,4,5,2,3,0,1],[1,0,3,2,5,4,7,6,9,8,11,10,13,12,15,14],[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15],[3,2,1,0,7,6,5,4,11,10,9,8,15,14,13,12],[2,3,0,1,6,7,4,5,10,11,8,9,14,15,12,13],[5,4,7,6,1,0,3,2,13,12,15,14,9,8,11,10],[4,5,6,7,0,1,2,3,12,13,14,15,8,9,10,11],[7,6,5,4,3,2,1,0,15,14,13,12,11,10,9,8],[6,7,4,5,2,3,0,1,14,15,12,13,10,11,8,9]],"identity":9,"divisor":16}。請依 [group_order, composite_divisor, element_order_rows, divisor_divides_order, exists_element_of_requested_order, boundary] 欄序回答。

查看答案與解釋(16, 16, [[0, 2], [1, 2], [2, 2], [3, 2], [4, 2], [5, 2], [6, 2], [7, 2], [8, 2], [9, 1], [10, 2], [11, 2], [12, 2], [13, 2], [14, 2], [15, 2]], 是, 否, composite_divisor_need_not_be_an_element_order)

Wave6第六層核對=(16, 16, [[0, 2], [1, 2], [2, 2], [3, 2], [4, 2], [5, 2], [6, 2], [7, 2], [8, 2], [9, 1], [10, 2], [11, 2], [12, 2], [13, 2], [14, 2], [15, 2]], 是, 否, composite_divisor_need_not_be_an_element_order)；依完整明示資料獨立重算；order-p witness必須同時驗g^p=e與所有1<=k<p皆有g^k!=e；完整有限枚舉只證指定model；composite divisor不保證是某元素的階。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261112-r01-cauchy-theorem-finite-groups-0097/)

有限群的Cauchy定理 · qf-mod43-cauchy-composite-divisor-boundary · candidate





## 98. 有限群的Cauchy定理

完整有限群、prime divisor與exact element-order證書。操作=cauchy-composite-divisor-boundary；資料={"group_table":[[10,11,8,9,14,15,12,13,2,3,0,1,6,7,4,5],[11,10,9,8,15,14,13,12,3,2,1,0,7,6,5,4],[8,9,10,11,12,13,14,15,0,1,2,3,4,5,6,7],[9,8,11,10,13,12,15,14,1,0,3,2,5,4,7,6],[14,15,12,13,10,11,8,9,6,7,4,5,2,3,0,1],[15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0],[12,13,14,15,8,9,10,11,4,5,6,7,0,1,2,3],[13,12,15,14,9,8,11,10,5,4,7,6,1,0,3,2],[2,3,0,1,6,7,4,5,10,11,8,9,14,15,12,13],[3,2,1,0,7,6,5,4,11,10,9,8,15,14,13,12],[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15],[1,0,3,2,5,4,7,6,9,8,11,10,13,12,15,14],[6,7,4,5,2,3,0,1,14,15,12,13,10,11,8,9],[7,6,5,4,3,2,1,0,15,14,13,12,11,10,9,8],[4,5,6,7,0,1,2,3,12,13,14,15,8,9,10,11],[5,4,7,6,1,0,3,2,13,12,15,14,9,8,11,10]],"identity":10,"divisor":16}。請依 [group_order, composite_divisor, element_order_rows, divisor_divides_order, exists_element_of_requested_order, boundary] 欄序回答。

查看答案與解釋(16, 16, [[0, 2], [1, 2], [2, 2], [3, 2], [4, 2], [5, 2], [6, 2], [7, 2], [8, 2], [9, 2], [10, 1], [11, 2], [12, 2], [13, 2], [14, 2], [15, 2]], 是, 否, composite_divisor_need_not_be_an_element_order)

Wave6第六層核對=(16, 16, [[0, 2], [1, 2], [2, 2], [3, 2], [4, 2], [5, 2], [6, 2], [7, 2], [8, 2], [9, 2], [10, 1], [11, 2], [12, 2], [13, 2], [14, 2], [15, 2]], 是, 否, composite_divisor_need_not_be_an_element_order)；依完整明示資料獨立重算；order-p witness必須同時驗g^p=e與所有1<=k<p皆有g^k!=e；完整有限枚舉只證指定model；composite divisor不保證是某元素的階。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261112-r01-cauchy-theorem-finite-groups-0098/)

有限群的Cauchy定理 · qf-mod43-cauchy-composite-divisor-boundary · candidate





## 99. 有限群的Cauchy定理

完整有限群、prime divisor與exact element-order證書。操作=cauchy-composite-divisor-boundary；資料={"group_table":[[11,10,9,8,15,14,13,12,3,2,1,0,7,6,5,4],[10,11,8,9,14,15,12,13,2,3,0,1,6,7,4,5],[9,8,11,10,13,12,15,14,1,0,3,2,5,4,7,6],[8,9,10,11,12,13,14,15,0,1,2,3,4,5,6,7],[15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0],[14,15,12,13,10,11,8,9,6,7,4,5,2,3,0,1],[13,12,15,14,9,8,11,10,5,4,7,6,1,0,3,2],[12,13,14,15,8,9,10,11,4,5,6,7,0,1,2,3],[3,2,1,0,7,6,5,4,11,10,9,8,15,14,13,12],[2,3,0,1,6,7,4,5,10,11,8,9,14,15,12,13],[1,0,3,2,5,4,7,6,9,8,11,10,13,12,15,14],[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15],[7,6,5,4,3,2,1,0,15,14,13,12,11,10,9,8],[6,7,4,5,2,3,0,1,14,15,12,13,10,11,8,9],[5,4,7,6,1,0,3,2,13,12,15,14,9,8,11,10],[4,5,6,7,0,1,2,3,12,13,14,15,8,9,10,11]],"identity":11,"divisor":16}。請依 [group_order, composite_divisor, element_order_rows, divisor_divides_order, exists_element_of_requested_order, boundary] 欄序回答。

查看答案與解釋(16, 16, [[0, 2], [1, 2], [2, 2], [3, 2], [4, 2], [5, 2], [6, 2], [7, 2], [8, 2], [9, 2], [10, 2], [11, 1], [12, 2], [13, 2], [14, 2], [15, 2]], 是, 否, composite_divisor_need_not_be_an_element_order)

Wave6第六層核對=(16, 16, [[0, 2], [1, 2], [2, 2], [3, 2], [4, 2], [5, 2], [6, 2], [7, 2], [8, 2], [9, 2], [10, 2], [11, 1], [12, 2], [13, 2], [14, 2], [15, 2]], 是, 否, composite_divisor_need_not_be_an_element_order)；依完整明示資料獨立重算；order-p witness必須同時驗g^p=e與所有1<=k<p皆有g^k!=e；完整有限枚舉只證指定model；composite divisor不保證是某元素的階。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261112-r01-cauchy-theorem-finite-groups-0099/)

有限群的Cauchy定理 · qf-mod43-cauchy-composite-divisor-boundary · candidate





## 100. 有限群的Cauchy定理

完整有限群、prime divisor與exact element-order證書。操作=cauchy-composite-divisor-boundary；資料={"group_table":[[12,13,14,15,8,9,10,11,4,5,6,7,0,1,2,3],[13,12,15,14,9,8,11,10,5,4,7,6,1,0,3,2],[14,15,12,13,10,11,8,9,6,7,4,5,2,3,0,1],[15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0],[8,9,10,11,12,13,14,15,0,1,2,3,4,5,6,7],[9,8,11,10,13,12,15,14,1,0,3,2,5,4,7,6],[10,11,8,9,14,15,12,13,2,3,0,1,6,7,4,5],[11,10,9,8,15,14,13,12,3,2,1,0,7,6,5,4],[4,5,6,7,0,1,2,3,12,13,14,15,8,9,10,11],[5,4,7,6,1,0,3,2,13,12,15,14,9,8,11,10],[6,7,4,5,2,3,0,1,14,15,12,13,10,11,8,9],[7,6,5,4,3,2,1,0,15,14,13,12,11,10,9,8],[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15],[1,0,3,2,5,4,7,6,9,8,11,10,13,12,15,14],[2,3,0,1,6,7,4,5,10,11,8,9,14,15,12,13],[3,2,1,0,7,6,5,4,11,10,9,8,15,14,13,12]],"identity":12,"divisor":16}。請依 [group_order, composite_divisor, element_order_rows, divisor_divides_order, exists_element_of_requested_order, boundary] 欄序回答。

查看答案與解釋(16, 16, [[0, 2], [1, 2], [2, 2], [3, 2], [4, 2], [5, 2], [6, 2], [7, 2], [8, 2], [9, 2], [10, 2], [11, 2], [12, 1], [13, 2], [14, 2], [15, 2]], 是, 否, composite_divisor_need_not_be_an_element_order)

Wave6第六層核對=(16, 16, [[0, 2], [1, 2], [2, 2], [3, 2], [4, 2], [5, 2], [6, 2], [7, 2], [8, 2], [9, 2], [10, 2], [11, 2], [12, 1], [13, 2], [14, 2], [15, 2]], 是, 否, composite_divisor_need_not_be_an_element_order)；依完整明示資料獨立重算；order-p witness必須同時驗g^p=e與所有1<=k<p皆有g^k!=e；完整有限枚舉只證指定model；composite divisor不保證是某元素的階。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261112-r01-cauchy-theorem-finite-groups-0100/)

有限群的Cauchy定理 · qf-mod43-cauchy-composite-divisor-boundary · candidate



[原始題目 JSONL](https://ocme.evemisslab.com/data/questions/batches/batch-20261014-advance-20261112-r01-cauchy-theorem-finite-groups-foundations/questions.jsonl) · [驗收報告](https://ocme.evemisslab.com/data/questions/batches/batch-20261014-advance-20261112-r01-cauchy-theorem-finite-groups-foundations/validation-report.json)