本批已通過 Schema、去重、來源快照與獨立答案重算；仍未標記為人工審定。
本題庫已有對應的中英逐步詳解。原題的 candidate 與英文 ai_candidate 狀態保留；AI 覆核、有限計算與 Lean 形式證明分開標示。
batch-20261014-advance-20261031-r06-finite-field-foundations · 2026-10-14 · 100 題
完整prime field Z_p運算。操作=fielddeep-characteristic；資料={"p":2}。請依 [p,successive_sums_of_one,characteristic,certificate] 欄序回答。
(2, [0, 1, 0], 2, additive_order_of_one)
Wave4收束核對=(2, [0, 1, 0], 2, additive_order_of_one)；依完整明示資料重算；只對非零元素取逆且永不除以零；有限域階為prime power但本題族不宣稱每個有限環為域。
有限域 · qf-mod31-fielddeep-characteristic · candidate
完整prime field Z_p運算。操作=fielddeep-characteristic；資料={"p":3}。請依 [p,successive_sums_of_one,characteristic,certificate] 欄序回答。
(3, [0, 1, 2, 0], 3, additive_order_of_one)
Wave4收束核對=(3, [0, 1, 2, 0], 3, additive_order_of_one)；依完整明示資料重算；只對非零元素取逆且永不除以零；有限域階為prime power但本題族不宣稱每個有限環為域。
有限域 · qf-mod31-fielddeep-characteristic · candidate
完整prime field Z_p運算。操作=fielddeep-characteristic；資料={"p":5}。請依 [p,successive_sums_of_one,characteristic,certificate] 欄序回答。
(5, [0, 1, 2, 3, 4, 0], 5, additive_order_of_one)
Wave4收束核對=(5, [0, 1, 2, 3, 4, 0], 5, additive_order_of_one)；依完整明示資料重算；只對非零元素取逆且永不除以零；有限域階為prime power但本題族不宣稱每個有限環為域。
有限域 · qf-mod31-fielddeep-characteristic · candidate
完整prime field Z_p運算。操作=fielddeep-characteristic；資料={"p":7}。請依 [p,successive_sums_of_one,characteristic,certificate] 欄序回答。
(7, [0, 1, 2, 3, 4, 5, 6, 0], 7, additive_order_of_one)
Wave4收束核對=(7, [0, 1, 2, 3, 4, 5, 6, 0], 7, additive_order_of_one)；依完整明示資料重算；只對非零元素取逆且永不除以零；有限域階為prime power但本題族不宣稱每個有限環為域。
有限域 · qf-mod31-fielddeep-characteristic · candidate
完整prime field Z_p運算。操作=fielddeep-characteristic；資料={"p":11}。請依 [p,successive_sums_of_one,characteristic,certificate] 欄序回答。
(11, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 0], 11, additive_order_of_one)
Wave4收束核對=(11, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 0], 11, additive_order_of_one)；依完整明示資料重算；只對非零元素取逆且永不除以零；有限域階為prime power但本題族不宣稱每個有限環為域。
有限域 · qf-mod31-fielddeep-characteristic · candidate
完整prime field Z_p運算。操作=fielddeep-characteristic；資料={"p":13}。請依 [p,successive_sums_of_one,characteristic,certificate] 欄序回答。
(13, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 0], 13, additive_order_of_one)
Wave4收束核對=(13, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 0], 13, additive_order_of_one)；依完整明示資料重算；只對非零元素取逆且永不除以零；有限域階為prime power但本題族不宣稱每個有限環為域。
有限域 · qf-mod31-fielddeep-characteristic · candidate
完整prime field Z_p運算。操作=fielddeep-characteristic；資料={"p":17}。請依 [p,successive_sums_of_one,characteristic,certificate] 欄序回答。
(17, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 0], 17, additive_order_of_one)
Wave4收束核對=(17, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 0], 17, additive_order_of_one)；依完整明示資料重算；只對非零元素取逆且永不除以零；有限域階為prime power但本題族不宣稱每個有限環為域。
有限域 · qf-mod31-fielddeep-characteristic · candidate
完整prime field Z_p運算。操作=fielddeep-characteristic；資料={"p":19}。請依 [p,successive_sums_of_one,characteristic,certificate] 欄序回答。
(19, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 0], 19, additive_order_of_one)
Wave4收束核對=(19, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 0], 19, additive_order_of_one)；依完整明示資料重算；只對非零元素取逆且永不除以零；有限域階為prime power但本題族不宣稱每個有限環為域。
有限域 · qf-mod31-fielddeep-characteristic · candidate
完整prime field Z_p運算。操作=fielddeep-characteristic；資料={"p":23}。請依 [p,successive_sums_of_one,characteristic,certificate] 欄序回答。
(23, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 0], 23, additive_order_of_one)
Wave4收束核對=(23, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 0], 23, additive_order_of_one)；依完整明示資料重算；只對非零元素取逆且永不除以零；有限域階為prime power但本題族不宣稱每個有限環為域。
有限域 · qf-mod31-fielddeep-characteristic · candidate
完整prime field Z_p運算。操作=fielddeep-characteristic；資料={"p":29}。請依 [p,successive_sums_of_one,characteristic,certificate] 欄序回答。
(29, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 0], 29, additive_order_of_one)
Wave4收束核對=(29, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 0], 29, additive_order_of_one)；依完整明示資料重算；只對非零元素取逆且永不除以零；有限域階為prime power但本題族不宣稱每個有限環為域。
有限域 · qf-mod31-fielddeep-characteristic · candidate
完整prime field Z_p運算。操作=fielddeep-characteristic；資料={"p":31}。請依 [p,successive_sums_of_one,characteristic,certificate] 欄序回答。
(31, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 0], 31, additive_order_of_one)
Wave4收束核對=(31, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 0], 31, additive_order_of_one)；依完整明示資料重算；只對非零元素取逆且永不除以零；有限域階為prime power但本題族不宣稱每個有限環為域。
有限域 · qf-mod31-fielddeep-characteristic · candidate
完整prime field Z_p運算。操作=fielddeep-characteristic；資料={"p":37}。請依 [p,successive_sums_of_one,characteristic,certificate] 欄序回答。
(37, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 0], 37, additive_order_of_one)
Wave4收束核對=(37, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 0], 37, additive_order_of_one)；依完整明示資料重算；只對非零元素取逆且永不除以零；有限域階為prime power但本題族不宣稱每個有限環為域。
有限域 · qf-mod31-fielddeep-characteristic · candidate
完整prime field Z_p運算。操作=fielddeep-characteristic；資料={"p":41}。請依 [p,successive_sums_of_one,characteristic,certificate] 欄序回答。
(41, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 0], 41, additive_order_of_one)
Wave4收束核對=(41, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 0], 41, additive_order_of_one)；依完整明示資料重算；只對非零元素取逆且永不除以零；有限域階為prime power但本題族不宣稱每個有限環為域。
有限域 · qf-mod31-fielddeep-characteristic · candidate
完整prime field Z_p運算。操作=fielddeep-characteristic；資料={"p":43}。請依 [p,successive_sums_of_one,characteristic,certificate] 欄序回答。
(43, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 0], 43, additive_order_of_one)
Wave4收束核對=(43, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 0], 43, additive_order_of_one)；依完整明示資料重算；只對非零元素取逆且永不除以零；有限域階為prime power但本題族不宣稱每個有限環為域。
有限域 · qf-mod31-fielddeep-characteristic · candidate
完整prime field Z_p運算。操作=fielddeep-characteristic；資料={"p":47}。請依 [p,successive_sums_of_one,characteristic,certificate] 欄序回答。
(47, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 0], 47, additive_order_of_one)
Wave4收束核對=(47, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 0], 47, additive_order_of_one)；依完整明示資料重算；只對非零元素取逆且永不除以零；有限域階為prime power但本題族不宣稱每個有限環為域。
有限域 · qf-mod31-fielddeep-characteristic · candidate
完整prime field Z_p運算。操作=fielddeep-characteristic；資料={"p":53}。請依 [p,successive_sums_of_one,characteristic,certificate] 欄序回答。
(53, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 0], 53, additive_order_of_one)
Wave4收束核對=(53, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 0], 53, additive_order_of_one)；依完整明示資料重算；只對非零元素取逆且永不除以零；有限域階為prime power但本題族不宣稱每個有限環為域。
有限域 · qf-mod31-fielddeep-characteristic · candidate
完整prime field Z_p運算。操作=fielddeep-characteristic；資料={"p":59}。請依 [p,successive_sums_of_one,characteristic,certificate] 欄序回答。
(59, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 0], 59, additive_order_of_one)
Wave4收束核對=(59, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 0], 59, additive_order_of_one)；依完整明示資料重算；只對非零元素取逆且永不除以零；有限域階為prime power但本題族不宣稱每個有限環為域。
有限域 · qf-mod31-fielddeep-characteristic · candidate
完整prime field Z_p運算。操作=fielddeep-characteristic；資料={"p":61}。請依 [p,successive_sums_of_one,characteristic,certificate] 欄序回答。
(61, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 0], 61, additive_order_of_one)
Wave4收束核對=(61, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 0], 61, additive_order_of_one)；依完整明示資料重算；只對非零元素取逆且永不除以零；有限域階為prime power但本題族不宣稱每個有限環為域。
有限域 · qf-mod31-fielddeep-characteristic · candidate
完整prime field Z_p運算。操作=fielddeep-characteristic；資料={"p":67}。請依 [p,successive_sums_of_one,characteristic,certificate] 欄序回答。
(67, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 0], 67, additive_order_of_one)
Wave4收束核對=(67, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 0], 67, additive_order_of_one)；依完整明示資料重算；只對非零元素取逆且永不除以零；有限域階為prime power但本題族不宣稱每個有限環為域。
有限域 · qf-mod31-fielddeep-characteristic · candidate
完整prime field Z_p運算。操作=fielddeep-characteristic；資料={"p":71}。請依 [p,successive_sums_of_one,characteristic,certificate] 欄序回答。
(71, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 0], 71, additive_order_of_one)
Wave4收束核對=(71, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 0], 71, additive_order_of_one)；依完整明示資料重算；只對非零元素取逆且永不除以零；有限域階為prime power但本題族不宣稱每個有限環為域。
有限域 · qf-mod31-fielddeep-characteristic · candidate
完整prime field Z_p運算。操作=fielddeep-characteristic；資料={"p":73}。請依 [p,successive_sums_of_one,characteristic,certificate] 欄序回答。
(73, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 0], 73, additive_order_of_one)
Wave4收束核對=(73, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 0], 73, additive_order_of_one)；依完整明示資料重算；只對非零元素取逆且永不除以零；有限域階為prime power但本題族不宣稱每個有限環為域。
有限域 · qf-mod31-fielddeep-characteristic · candidate
完整prime field Z_p運算。操作=fielddeep-characteristic；資料={"p":79}。請依 [p,successive_sums_of_one,characteristic,certificate] 欄序回答。
(79, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 0], 79, additive_order_of_one)
Wave4收束核對=(79, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 0], 79, additive_order_of_one)；依完整明示資料重算；只對非零元素取逆且永不除以零；有限域階為prime power但本題族不宣稱每個有限環為域。
有限域 · qf-mod31-fielddeep-characteristic · candidate
完整prime field Z_p運算。操作=fielddeep-characteristic；資料={"p":83}。請依 [p,successive_sums_of_one,characteristic,certificate] 欄序回答。
(83, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 0], 83, additive_order_of_one)
Wave4收束核對=(83, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 0], 83, additive_order_of_one)；依完整明示資料重算；只對非零元素取逆且永不除以零；有限域階為prime power但本題族不宣稱每個有限環為域。
有限域 · qf-mod31-fielddeep-characteristic · candidate
完整prime field Z_p運算。操作=fielddeep-characteristic；資料={"p":89}。請依 [p,successive_sums_of_one,characteristic,certificate] 欄序回答。
(89, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 0], 89, additive_order_of_one)
Wave4收束核對=(89, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 0], 89, additive_order_of_one)；依完整明示資料重算；只對非零元素取逆且永不除以零；有限域階為prime power但本題族不宣稱每個有限環為域。
有限域 · qf-mod31-fielddeep-characteristic · candidate
完整prime field Z_p運算。操作=fielddeep-characteristic；資料={"p":97}。請依 [p,successive_sums_of_one,characteristic,certificate] 欄序回答。
(97, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 0], 97, additive_order_of_one)
Wave4收束核對=(97, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 0], 97, additive_order_of_one)；依完整明示資料重算；只對非零元素取逆且永不除以零；有限域階為prime power但本題族不宣稱每個有限環為域。
有限域 · qf-mod31-fielddeep-characteristic · candidate
完整prime field Z_p運算。操作=fielddeep-power-cycle；資料={"p":2,"element":1}。請依 [element,powers,last,is_one,certificate] 欄序回答。
(1, [1], 1, 是, nonzero_multiplicative_group_cycle)
Wave4收束核對=(1, [1], 1, 是, nonzero_multiplicative_group_cycle)；依完整明示資料重算；只對非零元素取逆且永不除以零；有限域階為prime power但本題族不宣稱每個有限環為域。
有限域 · qf-mod31-fielddeep-power-cycle · candidate
完整prime field Z_p運算。操作=fielddeep-power-cycle；資料={"p":3,"element":2}。請依 [element,powers,last,is_one,certificate] 欄序回答。
(2, [2, 1], 1, 是, nonzero_multiplicative_group_cycle)
Wave4收束核對=(2, [2, 1], 1, 是, nonzero_multiplicative_group_cycle)；依完整明示資料重算；只對非零元素取逆且永不除以零；有限域階為prime power但本題族不宣稱每個有限環為域。
有限域 · qf-mod31-fielddeep-power-cycle · candidate
完整prime field Z_p運算。操作=fielddeep-power-cycle；資料={"p":5,"element":3}。請依 [element,powers,last,is_one,certificate] 欄序回答。
(3, [3, 4, 2, 1], 1, 是, nonzero_multiplicative_group_cycle)
Wave4收束核對=(3, [3, 4, 2, 1], 1, 是, nonzero_multiplicative_group_cycle)；依完整明示資料重算；只對非零元素取逆且永不除以零；有限域階為prime power但本題族不宣稱每個有限環為域。
有限域 · qf-mod31-fielddeep-power-cycle · candidate
完整prime field Z_p運算。操作=fielddeep-power-cycle；資料={"p":7,"element":4}。請依 [element,powers,last,is_one,certificate] 欄序回答。
(4, [4, 2, 1, 4, 2, 1], 1, 是, nonzero_multiplicative_group_cycle)
Wave4收束核對=(4, [4, 2, 1, 4, 2, 1], 1, 是, nonzero_multiplicative_group_cycle)；依完整明示資料重算；只對非零元素取逆且永不除以零；有限域階為prime power但本題族不宣稱每個有限環為域。
有限域 · qf-mod31-fielddeep-power-cycle · candidate
完整prime field Z_p運算。操作=fielddeep-power-cycle；資料={"p":11,"element":5}。請依 [element,powers,last,is_one,certificate] 欄序回答。
(5, [5, 3, 4, 9, 1, 5, 3, 4, 9, 1], 1, 是, nonzero_multiplicative_group_cycle)
Wave4收束核對=(5, [5, 3, 4, 9, 1, 5, 3, 4, 9, 1], 1, 是, nonzero_multiplicative_group_cycle)；依完整明示資料重算；只對非零元素取逆且永不除以零；有限域階為prime power但本題族不宣稱每個有限環為域。
有限域 · qf-mod31-fielddeep-power-cycle · candidate
完整prime field Z_p運算。操作=fielddeep-power-cycle；資料={"p":13,"element":6}。請依 [element,powers,last,is_one,certificate] 欄序回答。
(6, [6, 10, 8, 9, 2, 12, 7, 3, 5, 4, 11, 1], 1, 是, nonzero_multiplicative_group_cycle)
Wave4收束核對=(6, [6, 10, 8, 9, 2, 12, 7, 3, 5, 4, 11, 1], 1, 是, nonzero_multiplicative_group_cycle)；依完整明示資料重算；只對非零元素取逆且永不除以零；有限域階為prime power但本題族不宣稱每個有限環為域。
有限域 · qf-mod31-fielddeep-power-cycle · candidate
完整prime field Z_p運算。操作=fielddeep-power-cycle；資料={"p":17,"element":7}。請依 [element,powers,last,is_one,certificate] 欄序回答。
(7, [7, 15, 3, 4, 11, 9, 12, 16, 10, 2, 14, 13, 6, 8, 5, 1], 1, 是, nonzero_multiplicative_group_cycle)
Wave4收束核對=(7, [7, 15, 3, 4, 11, 9, 12, 16, 10, 2, 14, 13, 6, 8, 5, 1], 1, 是, nonzero_multiplicative_group_cycle)；依完整明示資料重算；只對非零元素取逆且永不除以零；有限域階為prime power但本題族不宣稱每個有限環為域。
有限域 · qf-mod31-fielddeep-power-cycle · candidate
完整prime field Z_p運算。操作=fielddeep-power-cycle；資料={"p":19,"element":8}。請依 [element,powers,last,is_one,certificate] 欄序回答。
(8, [8, 7, 18, 11, 12, 1, 8, 7, 18, 11, 12, 1, 8, 7, 18, 11, 12, 1], 1, 是, nonzero_multiplicative_group_cycle)
Wave4收束核對=(8, [8, 7, 18, 11, 12, 1, 8, 7, 18, 11, 12, 1, 8, 7, 18, 11, 12, 1], 1, 是, nonzero_multiplicative_group_cycle)；依完整明示資料重算；只對非零元素取逆且永不除以零；有限域階為prime power但本題族不宣稱每個有限環為域。
有限域 · qf-mod31-fielddeep-power-cycle · candidate
完整prime field Z_p運算。操作=fielddeep-power-cycle；資料={"p":23,"element":9}。請依 [element,powers,last,is_one,certificate] 欄序回答。
(9, [9, 12, 16, 6, 8, 3, 4, 13, 2, 18, 1, 9, 12, 16, 6, 8, 3, 4, 13, 2, 18, 1], 1, 是, nonzero_multiplicative_group_cycle)
Wave4收束核對=(9, [9, 12, 16, 6, 8, 3, 4, 13, 2, 18, 1, 9, 12, 16, 6, 8, 3, 4, 13, 2, 18, 1], 1, 是, nonzero_multiplicative_group_cycle)；依完整明示資料重算；只對非零元素取逆且永不除以零；有限域階為prime power但本題族不宣稱每個有限環為域。
有限域 · qf-mod31-fielddeep-power-cycle · candidate
完整prime field Z_p運算。操作=fielddeep-power-cycle；資料={"p":29,"element":10}。請依 [element,powers,last,is_one,certificate] 欄序回答。
(10, [10, 13, 14, 24, 8, 22, 17, 25, 18, 6, 2, 20, 26, 28, 19, 16, 15, 5, 21, 7, 12, 4, 11, 23, 27, 9, 3, 1], 1, 是, nonzero_multiplicative_group_cycle)
Wave4收束核對=(10, [10, 13, 14, 24, 8, 22, 17, 25, 18, 6, 2, 20, 26, 28, 19, 16, 15, 5, 21, 7, 12, 4, 11, 23, 27, 9, 3, 1], 1, 是, nonzero_multiplicative_group_cycle)；依完整明示資料重算；只對非零元素取逆且永不除以零；有限域階為prime power但本題族不宣稱每個有限環為域。
有限域 · qf-mod31-fielddeep-power-cycle · candidate
完整prime field Z_p運算。操作=fielddeep-power-cycle；資料={"p":31,"element":11}。請依 [element,powers,last,is_one,certificate] 欄序回答。
(11, [11, 28, 29, 9, 6, 4, 13, 19, 23, 5, 24, 16, 21, 14, 30, 20, 3, 2, 22, 25, 27, 18, 12, 8, 26, 7, 15, 10, 17, 1], 1, 是, nonzero_multiplicative_group_cycle)
Wave4收束核對=(11, [11, 28, 29, 9, 6, 4, 13, 19, 23, 5, 24, 16, 21, 14, 30, 20, 3, 2, 22, 25, 27, 18, 12, 8, 26, 7, 15, 10, 17, 1], 1, 是, nonzero_multiplicative_group_cycle)；依完整明示資料重算；只對非零元素取逆且永不除以零；有限域階為prime power但本題族不宣稱每個有限環為域。
有限域 · qf-mod31-fielddeep-power-cycle · candidate
完整prime field Z_p運算。操作=fielddeep-power-cycle；資料={"p":37,"element":12}。請依 [element,powers,last,is_one,certificate] 欄序回答。
(12, [12, 33, 26, 16, 7, 10, 9, 34, 1, 12, 33, 26, 16, 7, 10, 9, 34, 1, 12, 33, 26, 16, 7, 10, 9, 34, 1, 12, 33, 26, 16, 7, 10, 9, 34, 1], 1, 是, nonzero_multiplicative_group_cycle)
Wave4收束核對=(12, [12, 33, 26, 16, 7, 10, 9, 34, 1, 12, 33, 26, 16, 7, 10, 9, 34, 1, 12, 33, 26, 16, 7, 10, 9, 34, 1, 12, 33, 26, 16, 7, 10, 9, 34, 1], 1, 是, nonzero_multiplicative_group_cycle)；依完整明示資料重算；只對非零元素取逆且永不除以零；有限域階為prime power但本題族不宣稱每個有限環為域。
有限域 · qf-mod31-fielddeep-power-cycle · candidate
完整prime field Z_p運算。操作=fielddeep-power-cycle；資料={"p":41,"element":13}。請依 [element,powers,last,is_one,certificate] 欄序回答。
(13, [13, 5, 24, 25, 38, 2, 26, 10, 7, 9, 35, 4, 11, 20, 14, 18, 29, 8, 22, 40, 28, 36, 17, 16, 3, 39, 15, 31, 34, 32, 6, 37, 30, 21, 27, 23, 12, 33, 19, 1], 1, 是, nonzero_multiplicative_group_cycle)
Wave4收束核對=(13, [13, 5, 24, 25, 38, 2, 26, 10, 7, 9, 35, 4, 11, 20, 14, 18, 29, 8, 22, 40, 28, 36, 17, 16, 3, 39, 15, 31, 34, 32, 6, 37, 30, 21, 27, 23, 12, 33, 19, 1], 1, 是, nonzero_multiplicative_group_cycle)；依完整明示資料重算；只對非零元素取逆且永不除以零；有限域階為prime power但本題族不宣稱每個有限環為域。
有限域 · qf-mod31-fielddeep-power-cycle · candidate
完整prime field Z_p運算。操作=fielddeep-power-cycle；資料={"p":43,"element":14}。請依 [element,powers,last,is_one,certificate] 欄序回答。
(14, [14, 24, 35, 17, 23, 21, 36, 31, 4, 13, 10, 11, 25, 6, 41, 15, 38, 16, 9, 40, 1, 14, 24, 35, 17, 23, 21, 36, 31, 4, 13, 10, 11, 25, 6, 41, 15, 38, 16, 9, 40, 1], 1, 是, nonzero_multiplicative_group_cycle)
Wave4收束核對=(14, [14, 24, 35, 17, 23, 21, 36, 31, 4, 13, 10, 11, 25, 6, 41, 15, 38, 16, 9, 40, 1, 14, 24, 35, 17, 23, 21, 36, 31, 4, 13, 10, 11, 25, 6, 41, 15, 38, 16, 9, 40, 1], 1, 是, nonzero_multiplicative_group_cycle)；依完整明示資料重算；只對非零元素取逆且永不除以零；有限域階為prime power但本題族不宣稱每個有限環為域。
有限域 · qf-mod31-fielddeep-power-cycle · candidate
完整prime field Z_p運算。操作=fielddeep-power-cycle；資料={"p":47,"element":15}。請依 [element,powers,last,is_one,certificate] 欄序回答。
(15, [15, 37, 38, 6, 43, 34, 40, 36, 23, 16, 5, 28, 44, 2, 30, 27, 29, 12, 39, 21, 33, 25, 46, 32, 10, 9, 41, 4, 13, 7, 11, 24, 31, 42, 19, 3, 45, 17, 20, 18, 35, 8, 26, 14, 22, 1], 1, 是, nonzero_multiplicative_group_cycle)
Wave4收束核對=(15, [15, 37, 38, 6, 43, 34, 40, 36, 23, 16, 5, 28, 44, 2, 30, 27, 29, 12, 39, 21, 33, 25, 46, 32, 10, 9, 41, 4, 13, 7, 11, 24, 31, 42, 19, 3, 45, 17, 20, 18, 35, 8, 26, 14, 22, 1], 1, 是, nonzero_multiplicative_group_cycle)；依完整明示資料重算；只對非零元素取逆且永不除以零；有限域階為prime power但本題族不宣稱每個有限環為域。
有限域 · qf-mod31-fielddeep-power-cycle · candidate
完整prime field Z_p運算。操作=fielddeep-power-cycle；資料={"p":53,"element":16}。請依 [element,powers,last,is_one,certificate] 欄序回答。
(16, [16, 44, 15, 28, 24, 13, 49, 42, 36, 46, 47, 10, 1, 16, 44, 15, 28, 24, 13, 49, 42, 36, 46, 47, 10, 1, 16, 44, 15, 28, 24, 13, 49, 42, 36, 46, 47, 10, 1, 16, 44, 15, 28, 24, 13, 49, 42, 36, 46, 47, 10, 1], 1, 是, nonzero_multiplicative_group_cycle)
Wave4收束核對=(16, [16, 44, 15, 28, 24, 13, 49, 42, 36, 46, 47, 10, 1, 16, 44, 15, 28, 24, 13, 49, 42, 36, 46, 47, 10, 1, 16, 44, 15, 28, 24, 13, 49, 42, 36, 46, 47, 10, 1, 16, 44, 15, 28, 24, 13, 49, 42, 36, 46, 47, 10, 1], 1, 是, nonzero_multiplicative_group_cycle)；依完整明示資料重算；只對非零元素取逆且永不除以零；有限域階為prime power但本題族不宣稱每個有限環為域。
有限域 · qf-mod31-fielddeep-power-cycle · candidate
完整prime field Z_p運算。操作=fielddeep-power-cycle；資料={"p":59,"element":17}。請依 [element,powers,last,is_one,certificate] 欄序回答。
(17, [17, 53, 16, 36, 22, 20, 45, 57, 25, 12, 27, 46, 15, 19, 28, 4, 9, 35, 5, 26, 29, 21, 3, 51, 41, 48, 49, 7, 1, 17, 53, 16, 36, 22, 20, 45, 57, 25, 12, 27, 46, 15, 19, 28, 4, 9, 35, 5, 26, 29, 21, 3, 51, 41, 48, 49, 7, 1], 1, 是, nonzero_multiplicative_group_cycle)
Wave4收束核對=(17, [17, 53, 16, 36, 22, 20, 45, 57, 25, 12, 27, 46, 15, 19, 28, 4, 9, 35, 5, 26, 29, 21, 3, 51, 41, 48, 49, 7, 1, 17, 53, 16, 36, 22, 20, 45, 57, 25, 12, 27, 46, 15, 19, 28, 4, 9, 35, 5, 26, 29, 21, 3, 51, 41, 48, 49, 7, 1], 1, 是, nonzero_multiplicative_group_cycle)；依完整明示資料重算；只對非零元素取逆且永不除以零；有限域階為prime power但本題族不宣稱每個有限環為域。
有限域 · qf-mod31-fielddeep-power-cycle · candidate
完整prime field Z_p運算。操作=fielddeep-power-cycle；資料={"p":61,"element":18}。請依 [element,powers,last,is_one,certificate] 欄序回答。
(18, [18, 19, 37, 56, 32, 27, 59, 25, 23, 48, 10, 58, 7, 4, 11, 15, 26, 41, 6, 47, 53, 39, 31, 9, 40, 49, 28, 16, 44, 60, 43, 42, 24, 5, 29, 34, 2, 36, 38, 13, 51, 3, 54, 57, 50, 46, 35, 20, 55, 14, 8, 22, 30, 52, 21, 12, 33, 45, 17, 1], 1, 是, nonzero_multiplicative_group_cycle)
Wave4收束核對=(18, [18, 19, 37, 56, 32, 27, 59, 25, 23, 48, 10, 58, 7, 4, 11, 15, 26, 41, 6, 47, 53, 39, 31, 9, 40, 49, 28, 16, 44, 60, 43, 42, 24, 5, 29, 34, 2, 36, 38, 13, 51, 3, 54, 57, 50, 46, 35, 20, 55, 14, 8, 22, 30, 52, 21, 12, 33, 45, 17, 1], 1, 是, nonzero_multiplicative_group_cycle)；依完整明示資料重算；只對非零元素取逆且永不除以零；有限域階為prime power但本題族不宣稱每個有限環為域。
有限域 · qf-mod31-fielddeep-power-cycle · candidate
完整prime field Z_p運算。操作=fielddeep-power-cycle；資料={"p":67,"element":19}。請依 [element,powers,last,is_one,certificate] 欄序回答。
(19, [19, 26, 25, 6, 47, 22, 16, 36, 14, 65, 29, 15, 17, 55, 40, 23, 35, 62, 39, 4, 9, 37, 33, 24, 54, 21, 64, 10, 56, 59, 49, 60, 1, 19, 26, 25, 6, 47, 22, 16, 36, 14, 65, 29, 15, 17, 55, 40, 23, 35, 62, 39, 4, 9, 37, 33, 24, 54, 21, 64, 10, 56, 59, 49, 60, 1], 1, 是, nonzero_multiplicative_group_cycle)
Wave4收束核對=(19, [19, 26, 25, 6, 47, 22, 16, 36, 14, 65, 29, 15, 17, 55, 40, 23, 35, 62, 39, 4, 9, 37, 33, 24, 54, 21, 64, 10, 56, 59, 49, 60, 1, 19, 26, 25, 6, 47, 22, 16, 36, 14, 65, 29, 15, 17, 55, 40, 23, 35, 62, 39, 4, 9, 37, 33, 24, 54, 21, 64, 10, 56, 59, 49, 60, 1], 1, 是, nonzero_multiplicative_group_cycle)；依完整明示資料重算；只對非零元素取逆且永不除以零；有限域階為prime power但本題族不宣稱每個有限環為域。
有限域 · qf-mod31-fielddeep-power-cycle · candidate
完整prime field Z_p運算。操作=fielddeep-power-cycle；資料={"p":71,"element":20}。請依 [element,powers,last,is_one,certificate] 欄序回答。
(20, [20, 45, 48, 37, 30, 32, 1, 20, 45, 48, 37, 30, 32, 1, 20, 45, 48, 37, 30, 32, 1, 20, 45, 48, 37, 30, 32, 1, 20, 45, 48, 37, 30, 32, 1, 20, 45, 48, 37, 30, 32, 1, 20, 45, 48, 37, 30, 32, 1, 20, 45, 48, 37, 30, 32, 1, 20, 45, 48, 37, 30, 32, 1, 20, 45, 48, 37, 30, 32, 1], 1, 是, nonzero_multiplicative_group_cycle)
Wave4收束核對=(20, [20, 45, 48, 37, 30, 32, 1, 20, 45, 48, 37, 30, 32, 1, 20, 45, 48, 37, 30, 32, 1, 20, 45, 48, 37, 30, 32, 1, 20, 45, 48, 37, 30, 32, 1, 20, 45, 48, 37, 30, 32, 1, 20, 45, 48, 37, 30, 32, 1, 20, 45, 48, 37, 30, 32, 1, 20, 45, 48, 37, 30, 32, 1, 20, 45, 48, 37, 30, 32, 1], 1, 是, nonzero_multiplicative_group_cycle)；依完整明示資料重算；只對非零元素取逆且永不除以零；有限域階為prime power但本題族不宣稱每個有限環為域。
有限域 · qf-mod31-fielddeep-power-cycle · candidate
完整prime field Z_p運算。操作=fielddeep-power-cycle；資料={"p":73,"element":21}。請依 [element,powers,last,is_one,certificate] 欄序回答。
(21, [21, 3, 63, 9, 43, 27, 56, 8, 22, 24, 66, 72, 52, 70, 10, 64, 30, 46, 17, 65, 51, 49, 7, 1, 21, 3, 63, 9, 43, 27, 56, 8, 22, 24, 66, 72, 52, 70, 10, 64, 30, 46, 17, 65, 51, 49, 7, 1, 21, 3, 63, 9, 43, 27, 56, 8, 22, 24, 66, 72, 52, 70, 10, 64, 30, 46, 17, 65, 51, 49, 7, 1], 1, 是, nonzero_multiplicative_group_cycle)
Wave4收束核對=(21, [21, 3, 63, 9, 43, 27, 56, 8, 22, 24, 66, 72, 52, 70, 10, 64, 30, 46, 17, 65, 51, 49, 7, 1, 21, 3, 63, 9, 43, 27, 56, 8, 22, 24, 66, 72, 52, 70, 10, 64, 30, 46, 17, 65, 51, 49, 7, 1, 21, 3, 63, 9, 43, 27, 56, 8, 22, 24, 66, 72, 52, 70, 10, 64, 30, 46, 17, 65, 51, 49, 7, 1], 1, 是, nonzero_multiplicative_group_cycle)；依完整明示資料重算；只對非零元素取逆且永不除以零；有限域階為prime power但本題族不宣稱每個有限環為域。
有限域 · qf-mod31-fielddeep-power-cycle · candidate
完整prime field Z_p運算。操作=fielddeep-power-cycle；資料={"p":79,"element":22}。請依 [element,powers,last,is_one,certificate] 欄序回答。
(22, [22, 10, 62, 21, 67, 52, 38, 46, 64, 65, 8, 18, 1, 22, 10, 62, 21, 67, 52, 38, 46, 64, 65, 8, 18, 1, 22, 10, 62, 21, 67, 52, 38, 46, 64, 65, 8, 18, 1, 22, 10, 62, 21, 67, 52, 38, 46, 64, 65, 8, 18, 1, 22, 10, 62, 21, 67, 52, 38, 46, 64, 65, 8, 18, 1, 22, 10, 62, 21, 67, 52, 38, 46, 64, 65, 8, 18, 1], 1, 是, nonzero_multiplicative_group_cycle)
Wave4收束核對=(22, [22, 10, 62, 21, 67, 52, 38, 46, 64, 65, 8, 18, 1, 22, 10, 62, 21, 67, 52, 38, 46, 64, 65, 8, 18, 1, 22, 10, 62, 21, 67, 52, 38, 46, 64, 65, 8, 18, 1, 22, 10, 62, 21, 67, 52, 38, 46, 64, 65, 8, 18, 1, 22, 10, 62, 21, 67, 52, 38, 46, 64, 65, 8, 18, 1, 22, 10, 62, 21, 67, 52, 38, 46, 64, 65, 8, 18, 1], 1, 是, nonzero_multiplicative_group_cycle)；依完整明示資料重算；只對非零元素取逆且永不除以零；有限域階為prime power但本題族不宣稱每個有限環為域。
有限域 · qf-mod31-fielddeep-power-cycle · candidate
完整prime field Z_p運算。操作=fielddeep-power-cycle；資料={"p":83,"element":23}。請依 [element,powers,last,is_one,certificate] 欄序回答。
(23, [23, 31, 49, 48, 25, 77, 28, 63, 38, 44, 16, 36, 81, 37, 21, 68, 70, 33, 12, 27, 40, 7, 78, 51, 11, 4, 9, 41, 30, 26, 17, 59, 29, 3, 69, 10, 64, 61, 75, 65, 1, 23, 31, 49, 48, 25, 77, 28, 63, 38, 44, 16, 36, 81, 37, 21, 68, 70, 33, 12, 27, 40, 7, 78, 51, 11, 4, 9, 41, 30, 26, 17, 59, 29, 3, 69, 10, 64, 61, 75, 65, 1], 1, 是, nonzero_multiplicative_group_cycle)
Wave4收束核對=(23, [23, 31, 49, 48, 25, 77, 28, 63, 38, 44, 16, 36, 81, 37, 21, 68, 70, 33, 12, 27, 40, 7, 78, 51, 11, 4, 9, 41, 30, 26, 17, 59, 29, 3, 69, 10, 64, 61, 75, 65, 1, 23, 31, 49, 48, 25, 77, 28, 63, 38, 44, 16, 36, 81, 37, 21, 68, 70, 33, 12, 27, 40, 7, 78, 51, 11, 4, 9, 41, 30, 26, 17, 59, 29, 3, 69, 10, 64, 61, 75, 65, 1], 1, 是, nonzero_multiplicative_group_cycle)；依完整明示資料重算；只對非零元素取逆且永不除以零；有限域階為prime power但本題族不宣稱每個有限環為域。
有限域 · qf-mod31-fielddeep-power-cycle · candidate
完整prime field Z_p運算。操作=fielddeep-power-cycle；資料={"p":89,"element":24}。請依 [element,powers,last,is_one,certificate] 欄序回答。
(24, [24, 42, 29, 73, 61, 40, 70, 78, 3, 72, 37, 87, 41, 5, 31, 32, 56, 9, 38, 22, 83, 34, 15, 4, 7, 79, 27, 25, 66, 71, 13, 45, 12, 21, 59, 81, 75, 20, 35, 39, 46, 36, 63, 88, 65, 47, 60, 16, 28, 49, 19, 11, 86, 17, 52, 2, 48, 84, 58, 57, 33, 80, 51, 67, 6, 55, 74, 85, 82, 10, 62, 64, 23, 18, 76, 44, 77, 68, 30, 8, 14, 69, 54, 50, 43, 53, 26, 1], 1, 是, nonzero_multiplicative_group_cycle)
Wave4收束核對=(24, [24, 42, 29, 73, 61, 40, 70, 78, 3, 72, 37, 87, 41, 5, 31, 32, 56, 9, 38, 22, 83, 34, 15, 4, 7, 79, 27, 25, 66, 71, 13, 45, 12, 21, 59, 81, 75, 20, 35, 39, 46, 36, 63, 88, 65, 47, 60, 16, 28, 49, 19, 11, 86, 17, 52, 2, 48, 84, 58, 57, 33, 80, 51, 67, 6, 55, 74, 85, 82, 10, 62, 64, 23, 18, 76, 44, 77, 68, 30, 8, 14, 69, 54, 50, 43, 53, 26, 1], 1, 是, nonzero_multiplicative_group_cycle)；依完整明示資料重算；只對非零元素取逆且永不除以零；有限域階為prime power但本題族不宣稱每個有限環為域。
有限域 · qf-mod31-fielddeep-power-cycle · candidate
完整prime field Z_p運算。操作=fielddeep-power-cycle；資料={"p":97,"element":25}。請依 [element,powers,last,is_one,certificate] 欄序回答。
(25, [25, 43, 8, 6, 53, 64, 48, 36, 27, 93, 94, 22, 65, 73, 79, 35, 2, 50, 86, 16, 12, 9, 31, 96, 72, 54, 89, 91, 44, 33, 49, 61, 70, 4, 3, 75, 32, 24, 18, 62, 95, 47, 11, 81, 85, 88, 66, 1, 25, 43, 8, 6, 53, 64, 48, 36, 27, 93, 94, 22, 65, 73, 79, 35, 2, 50, 86, 16, 12, 9, 31, 96, 72, 54, 89, 91, 44, 33, 49, 61, 70, 4, 3, 75, 32, 24, 18, 62, 95, 47, 11, 81, 85, 88, 66, 1], 1, 是, nonzero_multiplicative_group_cycle)
Wave4收束核對=(25, [25, 43, 8, 6, 53, 64, 48, 36, 27, 93, 94, 22, 65, 73, 79, 35, 2, 50, 86, 16, 12, 9, 31, 96, 72, 54, 89, 91, 44, 33, 49, 61, 70, 4, 3, 75, 32, 24, 18, 62, 95, 47, 11, 81, 85, 88, 66, 1, 25, 43, 8, 6, 53, 64, 48, 36, 27, 93, 94, 22, 65, 73, 79, 35, 2, 50, 86, 16, 12, 9, 31, 96, 72, 54, 89, 91, 44, 33, 49, 61, 70, 4, 3, 75, 32, 24, 18, 62, 95, 47, 11, 81, 85, 88, 66, 1], 1, 是, nonzero_multiplicative_group_cycle)；依完整明示資料重算；只對非零元素取逆且永不除以零；有限域階為prime power但本題族不宣稱每個有限環為域。
有限域 · qf-mod31-fielddeep-power-cycle · candidate
完整prime field Z_p運算。操作=fielddeep-affine-solve；資料={"p":2,"a":1,"b":1,"c":1}。請依 [a,b,c,inverse,solution,substitution,unique] 欄序回答。
(1, 1, 1, 1, 0, 1, 是)
Wave4收束核對=(1, 1, 1, 1, 0, 1, 是)；依完整明示資料重算；只對非零元素取逆且永不除以零；有限域階為prime power但本題族不宣稱每個有限環為域。
有限域 · qf-mod31-fielddeep-affine-solve · candidate
完整prime field Z_p運算。操作=fielddeep-affine-solve；資料={"p":3,"a":2,"b":2,"c":0}。請依 [a,b,c,inverse,solution,substitution,unique] 欄序回答。
(2, 2, 0, 2, 2, 0, 是)
Wave4收束核對=(2, 2, 0, 2, 2, 0, 是)；依完整明示資料重算；只對非零元素取逆且永不除以零；有限域階為prime power但本題族不宣稱每個有限環為域。
有限域 · qf-mod31-fielddeep-affine-solve · candidate
完整prime field Z_p運算。操作=fielddeep-affine-solve；資料={"p":5,"a":3,"b":3,"c":0}。請依 [a,b,c,inverse,solution,substitution,unique] 欄序回答。
(3, 3, 0, 2, 4, 0, 是)
Wave4收束核對=(3, 3, 0, 2, 4, 0, 是)；依完整明示資料重算；只對非零元素取逆且永不除以零；有限域階為prime power但本題族不宣稱每個有限環為域。
有限域 · qf-mod31-fielddeep-affine-solve · candidate
完整prime field Z_p運算。操作=fielddeep-affine-solve；資料={"p":7,"a":4,"b":4,"c":0}。請依 [a,b,c,inverse,solution,substitution,unique] 欄序回答。
(4, 4, 0, 2, 6, 0, 是)
Wave4收束核對=(4, 4, 0, 2, 6, 0, 是)；依完整明示資料重算；只對非零元素取逆且永不除以零；有限域階為prime power但本題族不宣稱每個有限環為域。
有限域 · qf-mod31-fielddeep-affine-solve · candidate
完整prime field Z_p運算。操作=fielddeep-affine-solve；資料={"p":11,"a":5,"b":5,"c":9}。請依 [a,b,c,inverse,solution,substitution,unique] 欄序回答。
(5, 5, 9, 9, 3, 9, 是)
Wave4收束核對=(5, 5, 9, 9, 3, 9, 是)；依完整明示資料重算；只對非零元素取逆且永不除以零；有限域階為prime power但本題族不宣稱每個有限環為域。
有限域 · qf-mod31-fielddeep-affine-solve · candidate
完整prime field Z_p運算。操作=fielddeep-affine-solve；資料={"p":13,"a":6,"b":6,"c":11}。請依 [a,b,c,inverse,solution,substitution,unique] 欄序回答。
(6, 6, 11, 11, 3, 11, 是)
Wave4收束核對=(6, 6, 11, 11, 3, 11, 是)；依完整明示資料重算；只對非零元素取逆且永不除以零；有限域階為prime power但本題族不宣稱每個有限環為域。
有限域 · qf-mod31-fielddeep-affine-solve · candidate
完整prime field Z_p運算。操作=fielddeep-affine-solve；資料={"p":17,"a":7,"b":7,"c":13}。請依 [a,b,c,inverse,solution,substitution,unique] 欄序回答。
(7, 7, 13, 5, 13, 13, 是)
Wave4收束核對=(7, 7, 13, 5, 13, 13, 是)；依完整明示資料重算；只對非零元素取逆且永不除以零；有限域階為prime power但本題族不宣稱每個有限環為域。
有限域 · qf-mod31-fielddeep-affine-solve · candidate
完整prime field Z_p運算。操作=fielddeep-affine-solve；資料={"p":19,"a":8,"b":8,"c":15}。請依 [a,b,c,inverse,solution,substitution,unique] 欄序回答。
(8, 8, 15, 12, 8, 15, 是)
Wave4收束核對=(8, 8, 15, 12, 8, 15, 是)；依完整明示資料重算；只對非零元素取逆且永不除以零；有限域階為prime power但本題族不宣稱每個有限環為域。
有限域 · qf-mod31-fielddeep-affine-solve · candidate
完整prime field Z_p運算。操作=fielddeep-affine-solve；資料={"p":23,"a":9,"b":9,"c":17}。請依 [a,b,c,inverse,solution,substitution,unique] 欄序回答。
(9, 9, 17, 18, 6, 17, 是)
Wave4收束核對=(9, 9, 17, 18, 6, 17, 是)；依完整明示資料重算；只對非零元素取逆且永不除以零；有限域階為prime power但本題族不宣稱每個有限環為域。
有限域 · qf-mod31-fielddeep-affine-solve · candidate
完整prime field Z_p運算。操作=fielddeep-affine-solve；資料={"p":29,"a":10,"b":10,"c":19}。請依 [a,b,c,inverse,solution,substitution,unique] 欄序回答。
(10, 10, 19, 3, 27, 19, 是)
Wave4收束核對=(10, 10, 19, 3, 27, 19, 是)；依完整明示資料重算；只對非零元素取逆且永不除以零；有限域階為prime power但本題族不宣稱每個有限環為域。
有限域 · qf-mod31-fielddeep-affine-solve · candidate
完整prime field Z_p運算。操作=fielddeep-affine-solve；資料={"p":31,"a":11,"b":11,"c":21}。請依 [a,b,c,inverse,solution,substitution,unique] 欄序回答。
(11, 11, 21, 17, 15, 21, 是)
Wave4收束核對=(11, 11, 21, 17, 15, 21, 是)；依完整明示資料重算；只對非零元素取逆且永不除以零；有限域階為prime power但本題族不宣稱每個有限環為域。
有限域 · qf-mod31-fielddeep-affine-solve · candidate
完整prime field Z_p運算。操作=fielddeep-affine-solve；資料={"p":37,"a":12,"b":12,"c":23}。請依 [a,b,c,inverse,solution,substitution,unique] 欄序回答。
(12, 12, 23, 34, 4, 23, 是)
Wave4收束核對=(12, 12, 23, 34, 4, 23, 是)；依完整明示資料重算；只對非零元素取逆且永不除以零；有限域階為prime power但本題族不宣稱每個有限環為域。
有限域 · qf-mod31-fielddeep-affine-solve · candidate
完整prime field Z_p運算。操作=fielddeep-affine-solve；資料={"p":41,"a":13,"b":13,"c":25}。請依 [a,b,c,inverse,solution,substitution,unique] 欄序回答。
(13, 13, 25, 19, 23, 25, 是)
Wave4收束核對=(13, 13, 25, 19, 23, 25, 是)；依完整明示資料重算；只對非零元素取逆且永不除以零；有限域階為prime power但本題族不宣稱每個有限環為域。
有限域 · qf-mod31-fielddeep-affine-solve · candidate
完整prime field Z_p運算。操作=fielddeep-affine-solve；資料={"p":43,"a":14,"b":14,"c":27}。請依 [a,b,c,inverse,solution,substitution,unique] 欄序回答。
(14, 14, 27, 40, 4, 27, 是)
Wave4收束核對=(14, 14, 27, 40, 4, 27, 是)；依完整明示資料重算；只對非零元素取逆且永不除以零；有限域階為prime power但本題族不宣稱每個有限環為域。
有限域 · qf-mod31-fielddeep-affine-solve · candidate
完整prime field Z_p運算。操作=fielddeep-affine-solve；資料={"p":47,"a":15,"b":15,"c":29}。請依 [a,b,c,inverse,solution,substitution,unique] 欄序回答。
(15, 15, 29, 22, 26, 29, 是)
Wave4收束核對=(15, 15, 29, 22, 26, 29, 是)；依完整明示資料重算；只對非零元素取逆且永不除以零；有限域階為prime power但本題族不宣稱每個有限環為域。
有限域 · qf-mod31-fielddeep-affine-solve · candidate
完整prime field Z_p運算。操作=fielddeep-affine-solve；資料={"p":53,"a":16,"b":16,"c":31}。請依 [a,b,c,inverse,solution,substitution,unique] 欄序回答。
(16, 16, 31, 10, 44, 31, 是)
Wave4收束核對=(16, 16, 31, 10, 44, 31, 是)；依完整明示資料重算；只對非零元素取逆且永不除以零；有限域階為prime power但本題族不宣稱每個有限環為域。
有限域 · qf-mod31-fielddeep-affine-solve · candidate
完整prime field Z_p運算。操作=fielddeep-affine-solve；資料={"p":59,"a":17,"b":17,"c":33}。請依 [a,b,c,inverse,solution,substitution,unique] 欄序回答。
(17, 17, 33, 7, 53, 33, 是)
Wave4收束核對=(17, 17, 33, 7, 53, 33, 是)；依完整明示資料重算；只對非零元素取逆且永不除以零；有限域階為prime power但本題族不宣稱每個有限環為域。
有限域 · qf-mod31-fielddeep-affine-solve · candidate
完整prime field Z_p運算。操作=fielddeep-affine-solve；資料={"p":61,"a":18,"b":18,"c":35}。請依 [a,b,c,inverse,solution,substitution,unique] 欄序回答。
(18, 18, 35, 17, 45, 35, 是)
Wave4收束核對=(18, 18, 35, 17, 45, 35, 是)；依完整明示資料重算；只對非零元素取逆且永不除以零；有限域階為prime power但本題族不宣稱每個有限環為域。
有限域 · qf-mod31-fielddeep-affine-solve · candidate
完整prime field Z_p運算。操作=fielddeep-affine-solve；資料={"p":67,"a":19,"b":19,"c":37}。請依 [a,b,c,inverse,solution,substitution,unique] 欄序回答。
(19, 19, 37, 60, 8, 37, 是)
Wave4收束核對=(19, 19, 37, 60, 8, 37, 是)；依完整明示資料重算；只對非零元素取逆且永不除以零；有限域階為prime power但本題族不宣稱每個有限環為域。
有限域 · qf-mod31-fielddeep-affine-solve · candidate
完整prime field Z_p運算。操作=fielddeep-affine-solve；資料={"p":71,"a":20,"b":20,"c":39}。請依 [a,b,c,inverse,solution,substitution,unique] 欄序回答。
(20, 20, 39, 32, 40, 39, 是)
Wave4收束核對=(20, 20, 39, 32, 40, 39, 是)；依完整明示資料重算；只對非零元素取逆且永不除以零；有限域階為prime power但本題族不宣稱每個有限環為域。
有限域 · qf-mod31-fielddeep-affine-solve · candidate
完整prime field Z_p運算。操作=fielddeep-affine-solve；資料={"p":73,"a":21,"b":21,"c":41}。請依 [a,b,c,inverse,solution,substitution,unique] 欄序回答。
(21, 21, 41, 7, 67, 41, 是)
Wave4收束核對=(21, 21, 41, 7, 67, 41, 是)；依完整明示資料重算；只對非零元素取逆且永不除以零；有限域階為prime power但本題族不宣稱每個有限環為域。
有限域 · qf-mod31-fielddeep-affine-solve · candidate
完整prime field Z_p運算。操作=fielddeep-affine-solve；資料={"p":79,"a":22,"b":22,"c":43}。請依 [a,b,c,inverse,solution,substitution,unique] 欄序回答。
(22, 22, 43, 18, 62, 43, 是)
Wave4收束核對=(22, 22, 43, 18, 62, 43, 是)；依完整明示資料重算；只對非零元素取逆且永不除以零；有限域階為prime power但本題族不宣稱每個有限環為域。
有限域 · qf-mod31-fielddeep-affine-solve · candidate
完整prime field Z_p運算。操作=fielddeep-affine-solve；資料={"p":83,"a":23,"b":23,"c":45}。請依 [a,b,c,inverse,solution,substitution,unique] 欄序回答。
(23, 23, 45, 65, 19, 45, 是)
Wave4收束核對=(23, 23, 45, 65, 19, 45, 是)；依完整明示資料重算；只對非零元素取逆且永不除以零；有限域階為prime power但本題族不宣稱每個有限環為域。
有限域 · qf-mod31-fielddeep-affine-solve · candidate
完整prime field Z_p運算。操作=fielddeep-affine-solve；資料={"p":89,"a":24,"b":24,"c":47}。請依 [a,b,c,inverse,solution,substitution,unique] 欄序回答。
(24, 24, 47, 26, 64, 47, 是)
Wave4收束核對=(24, 24, 47, 26, 64, 47, 是)；依完整明示資料重算；只對非零元素取逆且永不除以零；有限域階為prime power但本題族不宣稱每個有限環為域。
有限域 · qf-mod31-fielddeep-affine-solve · candidate
完整prime field Z_p運算。操作=fielddeep-affine-solve；資料={"p":97,"a":25,"b":25,"c":49}。請依 [a,b,c,inverse,solution,substitution,unique] 欄序回答。
(25, 25, 49, 66, 32, 49, 是)
Wave4收束核對=(25, 25, 49, 66, 32, 49, 是)；依完整明示資料重算；只對非零元素取逆且永不除以零；有限域階為prime power但本題族不宣稱每個有限環為域。
有限域 · qf-mod31-fielddeep-affine-solve · candidate
完整prime field Z_p運算。操作=fielddeep-frobenius；資料={"p":2,"element":0}。請依 [element,p,power,equal,certificate] 欄序回答。
(0, 2, 0, 是, Frobenius_on_prime_field)
Wave4收束核對=(0, 2, 0, 是, Frobenius_on_prime_field)；依完整明示資料重算；只對非零元素取逆且永不除以零；有限域階為prime power但本題族不宣稱每個有限環為域。
有限域 · qf-mod31-fielddeep-frobenius · candidate
完整prime field Z_p運算。操作=fielddeep-frobenius；資料={"p":3,"element":1}。請依 [element,p,power,equal,certificate] 欄序回答。
(1, 3, 1, 是, Frobenius_on_prime_field)
Wave4收束核對=(1, 3, 1, 是, Frobenius_on_prime_field)；依完整明示資料重算；只對非零元素取逆且永不除以零；有限域階為prime power但本題族不宣稱每個有限環為域。
有限域 · qf-mod31-fielddeep-frobenius · candidate
完整prime field Z_p運算。操作=fielddeep-frobenius；資料={"p":5,"element":2}。請依 [element,p,power,equal,certificate] 欄序回答。
(2, 5, 2, 是, Frobenius_on_prime_field)
Wave4收束核對=(2, 5, 2, 是, Frobenius_on_prime_field)；依完整明示資料重算；只對非零元素取逆且永不除以零；有限域階為prime power但本題族不宣稱每個有限環為域。
有限域 · qf-mod31-fielddeep-frobenius · candidate
完整prime field Z_p運算。操作=fielddeep-frobenius；資料={"p":7,"element":3}。請依 [element,p,power,equal,certificate] 欄序回答。
(3, 7, 3, 是, Frobenius_on_prime_field)
Wave4收束核對=(3, 7, 3, 是, Frobenius_on_prime_field)；依完整明示資料重算；只對非零元素取逆且永不除以零；有限域階為prime power但本題族不宣稱每個有限環為域。
有限域 · qf-mod31-fielddeep-frobenius · candidate
完整prime field Z_p運算。操作=fielddeep-frobenius；資料={"p":11,"element":4}。請依 [element,p,power,equal,certificate] 欄序回答。
(4, 11, 4, 是, Frobenius_on_prime_field)
Wave4收束核對=(4, 11, 4, 是, Frobenius_on_prime_field)；依完整明示資料重算；只對非零元素取逆且永不除以零；有限域階為prime power但本題族不宣稱每個有限環為域。
有限域 · qf-mod31-fielddeep-frobenius · candidate
完整prime field Z_p運算。操作=fielddeep-frobenius；資料={"p":13,"element":5}。請依 [element,p,power,equal,certificate] 欄序回答。
(5, 13, 5, 是, Frobenius_on_prime_field)
Wave4收束核對=(5, 13, 5, 是, Frobenius_on_prime_field)；依完整明示資料重算；只對非零元素取逆且永不除以零；有限域階為prime power但本題族不宣稱每個有限環為域。
有限域 · qf-mod31-fielddeep-frobenius · candidate
完整prime field Z_p運算。操作=fielddeep-frobenius；資料={"p":17,"element":6}。請依 [element,p,power,equal,certificate] 欄序回答。
(6, 17, 6, 是, Frobenius_on_prime_field)
Wave4收束核對=(6, 17, 6, 是, Frobenius_on_prime_field)；依完整明示資料重算；只對非零元素取逆且永不除以零；有限域階為prime power但本題族不宣稱每個有限環為域。
有限域 · qf-mod31-fielddeep-frobenius · candidate
完整prime field Z_p運算。操作=fielddeep-frobenius；資料={"p":19,"element":7}。請依 [element,p,power,equal,certificate] 欄序回答。
(7, 19, 7, 是, Frobenius_on_prime_field)
Wave4收束核對=(7, 19, 7, 是, Frobenius_on_prime_field)；依完整明示資料重算；只對非零元素取逆且永不除以零；有限域階為prime power但本題族不宣稱每個有限環為域。
有限域 · qf-mod31-fielddeep-frobenius · candidate
完整prime field Z_p運算。操作=fielddeep-frobenius；資料={"p":23,"element":8}。請依 [element,p,power,equal,certificate] 欄序回答。
(8, 23, 8, 是, Frobenius_on_prime_field)
Wave4收束核對=(8, 23, 8, 是, Frobenius_on_prime_field)；依完整明示資料重算；只對非零元素取逆且永不除以零；有限域階為prime power但本題族不宣稱每個有限環為域。
有限域 · qf-mod31-fielddeep-frobenius · candidate
完整prime field Z_p運算。操作=fielddeep-frobenius；資料={"p":29,"element":9}。請依 [element,p,power,equal,certificate] 欄序回答。
(9, 29, 9, 是, Frobenius_on_prime_field)
Wave4收束核對=(9, 29, 9, 是, Frobenius_on_prime_field)；依完整明示資料重算；只對非零元素取逆且永不除以零；有限域階為prime power但本題族不宣稱每個有限環為域。
有限域 · qf-mod31-fielddeep-frobenius · candidate
完整prime field Z_p運算。操作=fielddeep-frobenius；資料={"p":31,"element":10}。請依 [element,p,power,equal,certificate] 欄序回答。
(10, 31, 10, 是, Frobenius_on_prime_field)
Wave4收束核對=(10, 31, 10, 是, Frobenius_on_prime_field)；依完整明示資料重算；只對非零元素取逆且永不除以零；有限域階為prime power但本題族不宣稱每個有限環為域。
有限域 · qf-mod31-fielddeep-frobenius · candidate
完整prime field Z_p運算。操作=fielddeep-frobenius；資料={"p":37,"element":11}。請依 [element,p,power,equal,certificate] 欄序回答。
(11, 37, 11, 是, Frobenius_on_prime_field)
Wave4收束核對=(11, 37, 11, 是, Frobenius_on_prime_field)；依完整明示資料重算；只對非零元素取逆且永不除以零；有限域階為prime power但本題族不宣稱每個有限環為域。
有限域 · qf-mod31-fielddeep-frobenius · candidate
完整prime field Z_p運算。操作=fielddeep-frobenius；資料={"p":41,"element":12}。請依 [element,p,power,equal,certificate] 欄序回答。
(12, 41, 12, 是, Frobenius_on_prime_field)
Wave4收束核對=(12, 41, 12, 是, Frobenius_on_prime_field)；依完整明示資料重算；只對非零元素取逆且永不除以零；有限域階為prime power但本題族不宣稱每個有限環為域。
有限域 · qf-mod31-fielddeep-frobenius · candidate
完整prime field Z_p運算。操作=fielddeep-frobenius；資料={"p":43,"element":13}。請依 [element,p,power,equal,certificate] 欄序回答。
(13, 43, 13, 是, Frobenius_on_prime_field)
Wave4收束核對=(13, 43, 13, 是, Frobenius_on_prime_field)；依完整明示資料重算；只對非零元素取逆且永不除以零；有限域階為prime power但本題族不宣稱每個有限環為域。
有限域 · qf-mod31-fielddeep-frobenius · candidate
完整prime field Z_p運算。操作=fielddeep-frobenius；資料={"p":47,"element":14}。請依 [element,p,power,equal,certificate] 欄序回答。
(14, 47, 14, 是, Frobenius_on_prime_field)
Wave4收束核對=(14, 47, 14, 是, Frobenius_on_prime_field)；依完整明示資料重算；只對非零元素取逆且永不除以零；有限域階為prime power但本題族不宣稱每個有限環為域。
有限域 · qf-mod31-fielddeep-frobenius · candidate
完整prime field Z_p運算。操作=fielddeep-frobenius；資料={"p":53,"element":15}。請依 [element,p,power,equal,certificate] 欄序回答。
(15, 53, 15, 是, Frobenius_on_prime_field)
Wave4收束核對=(15, 53, 15, 是, Frobenius_on_prime_field)；依完整明示資料重算；只對非零元素取逆且永不除以零；有限域階為prime power但本題族不宣稱每個有限環為域。
有限域 · qf-mod31-fielddeep-frobenius · candidate
完整prime field Z_p運算。操作=fielddeep-frobenius；資料={"p":59,"element":16}。請依 [element,p,power,equal,certificate] 欄序回答。
(16, 59, 16, 是, Frobenius_on_prime_field)
Wave4收束核對=(16, 59, 16, 是, Frobenius_on_prime_field)；依完整明示資料重算；只對非零元素取逆且永不除以零；有限域階為prime power但本題族不宣稱每個有限環為域。
有限域 · qf-mod31-fielddeep-frobenius · candidate
完整prime field Z_p運算。操作=fielddeep-frobenius；資料={"p":61,"element":17}。請依 [element,p,power,equal,certificate] 欄序回答。
(17, 61, 17, 是, Frobenius_on_prime_field)
Wave4收束核對=(17, 61, 17, 是, Frobenius_on_prime_field)；依完整明示資料重算；只對非零元素取逆且永不除以零；有限域階為prime power但本題族不宣稱每個有限環為域。
有限域 · qf-mod31-fielddeep-frobenius · candidate
完整prime field Z_p運算。操作=fielddeep-frobenius；資料={"p":67,"element":18}。請依 [element,p,power,equal,certificate] 欄序回答。
(18, 67, 18, 是, Frobenius_on_prime_field)
Wave4收束核對=(18, 67, 18, 是, Frobenius_on_prime_field)；依完整明示資料重算；只對非零元素取逆且永不除以零；有限域階為prime power但本題族不宣稱每個有限環為域。
有限域 · qf-mod31-fielddeep-frobenius · candidate
完整prime field Z_p運算。操作=fielddeep-frobenius；資料={"p":71,"element":19}。請依 [element,p,power,equal,certificate] 欄序回答。
(19, 71, 19, 是, Frobenius_on_prime_field)
Wave4收束核對=(19, 71, 19, 是, Frobenius_on_prime_field)；依完整明示資料重算；只對非零元素取逆且永不除以零；有限域階為prime power但本題族不宣稱每個有限環為域。
有限域 · qf-mod31-fielddeep-frobenius · candidate
完整prime field Z_p運算。操作=fielddeep-frobenius；資料={"p":73,"element":20}。請依 [element,p,power,equal,certificate] 欄序回答。
(20, 73, 20, 是, Frobenius_on_prime_field)
Wave4收束核對=(20, 73, 20, 是, Frobenius_on_prime_field)；依完整明示資料重算；只對非零元素取逆且永不除以零；有限域階為prime power但本題族不宣稱每個有限環為域。
有限域 · qf-mod31-fielddeep-frobenius · candidate
完整prime field Z_p運算。操作=fielddeep-frobenius；資料={"p":79,"element":21}。請依 [element,p,power,equal,certificate] 欄序回答。
(21, 79, 21, 是, Frobenius_on_prime_field)
Wave4收束核對=(21, 79, 21, 是, Frobenius_on_prime_field)；依完整明示資料重算；只對非零元素取逆且永不除以零；有限域階為prime power但本題族不宣稱每個有限環為域。
有限域 · qf-mod31-fielddeep-frobenius · candidate
完整prime field Z_p運算。操作=fielddeep-frobenius；資料={"p":83,"element":22}。請依 [element,p,power,equal,certificate] 欄序回答。
(22, 83, 22, 是, Frobenius_on_prime_field)
Wave4收束核對=(22, 83, 22, 是, Frobenius_on_prime_field)；依完整明示資料重算；只對非零元素取逆且永不除以零；有限域階為prime power但本題族不宣稱每個有限環為域。
有限域 · qf-mod31-fielddeep-frobenius · candidate
完整prime field Z_p運算。操作=fielddeep-frobenius；資料={"p":89,"element":23}。請依 [element,p,power,equal,certificate] 欄序回答。
(23, 89, 23, 是, Frobenius_on_prime_field)
Wave4收束核對=(23, 89, 23, 是, Frobenius_on_prime_field)；依完整明示資料重算；只對非零元素取逆且永不除以零；有限域階為prime power但本題族不宣稱每個有限環為域。
有限域 · qf-mod31-fielddeep-frobenius · candidate
完整prime field Z_p運算。操作=fielddeep-frobenius；資料={"p":97,"element":24}。請依 [element,p,power,equal,certificate] 欄序回答。
(24, 97, 24, 是, Frobenius_on_prime_field)
Wave4收束核對=(24, 97, 24, 是, Frobenius_on_prime_field)；依完整明示資料重算；只對非零元素取逆且永不除以零；有限域階為prime power但本題族不宣稱每個有限環為域。
有限域 · qf-mod31-fielddeep-frobenius · candidate