有限群的Cauchy定理基礎 · 脈衝 R01
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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
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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。
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(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）
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。
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(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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
有限群的Cauchy定理 · qf-mod43-cauchy-composite-divisor-boundary · candidate
原始題目 JSONL · 驗收報告