第 27722 題：Wilson定理

原題與已知條件

n>1、factorial congruence與prime-residue inverse pairing責任。操作=wilson-boundary；資料={"mode":"fermat_confusion","n":79}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。

• G001 — n>1、factorial congruence與prime-residue inverse pairing責任。操作=wilson-boundary；資料={"mode":"fermat_confusion","n":79}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。

定義與適用範圍

沿用原題明示的論域、假設與來源 MKO 定義。本題已完成第二對話數理與中英語義覆核，並由原始參數逐題獨立重算模型、答案與每個算術步驟；原題仍為 candidate。

• mko-wilson-theorem

逐步推導

source roles = [wilson-boundary]

derived = [[mode, n, running_factorial_residues, factorial_residue, minus_one_residue, Wilson_congruence, Wilson_statement, Fermat_statement, theorem_identification_claim, boundary]]

Wilson boundary ORIGINAL prime ORIGINAL running factorial product1 := mul(1, 1)

Wilson boundary ORIGINAL prime ORIGINAL running factorial product1 = 1

source roles = [Wilson boundary ORIGINAL prime, 79, 1, 1, 1]

derived = [0, 1, 是, 是]

Wilson boundary ORIGINAL prime ORIGINAL running factorial product2 := mul(1, 2)

Wilson boundary ORIGINAL prime ORIGINAL running factorial product2 = 2

source roles = [Wilson boundary ORIGINAL prime, 79, 2, 1, 2]

derived = [0, 2, 是, 是]

Wilson boundary ORIGINAL prime ORIGINAL running factorial product3 := mul(2, 3)

Wilson boundary ORIGINAL prime ORIGINAL running factorial product3 = 6

source roles = [Wilson boundary ORIGINAL prime, 79, 3, 2, 6]

derived = [0, 6, 是, 是]

Wilson boundary ORIGINAL prime ORIGINAL running factorial product4 := mul(6, 4)

Wilson boundary ORIGINAL prime ORIGINAL running factorial product4 = 24

source roles = [Wilson boundary ORIGINAL prime, 79, 4, 6, 24]

derived = [0, 24, 是, 是]

Wilson boundary ORIGINAL prime ORIGINAL running factorial product5 := mul(24, 5)

Wilson boundary ORIGINAL prime ORIGINAL running factorial product5 = 120

source roles = [Wilson boundary ORIGINAL prime, 79, 5, 24, 120]

derived = [1, 41, 是, 是]

Wilson boundary ORIGINAL prime ORIGINAL running factorial product6 := mul(41, 6)

Wilson boundary ORIGINAL prime ORIGINAL running factorial product6 = 246

source roles = [Wilson boundary ORIGINAL prime, 79, 6, 41, 246]

derived = [3, 9, 是, 是]

Wilson boundary ORIGINAL prime ORIGINAL running factorial product7 := mul(9, 7)

Wilson boundary ORIGINAL prime ORIGINAL running factorial product7 = 63

source roles = [Wilson boundary ORIGINAL prime, 79, 7, 9, 63]

derived = [0, 63, 是, 是]

Wilson boundary ORIGINAL prime ORIGINAL running factorial product8 := mul(63, 8)

Wilson boundary ORIGINAL prime ORIGINAL running factorial product8 = 504

source roles = [Wilson boundary ORIGINAL prime, 79, 8, 63, 504]

derived = [6, 30, 是, 是]

Wilson boundary ORIGINAL prime ORIGINAL running factorial product9 := mul(30, 9)

Wilson boundary ORIGINAL prime ORIGINAL running factorial product9 = 270

source roles = [Wilson boundary ORIGINAL prime, 79, 9, 30, 270]

derived = [3, 33, 是, 是]

Wilson boundary ORIGINAL prime ORIGINAL running factorial product10 := mul(33, 10)

Wilson boundary ORIGINAL prime ORIGINAL running factorial product10 = 330

source roles = [Wilson boundary ORIGINAL prime, 79, 10, 33, 330]

derived = [4, 14, 是, 是]

Wilson boundary ORIGINAL prime ORIGINAL running factorial product11 := mul(14, 11)

Wilson boundary ORIGINAL prime ORIGINAL running factorial product11 = 154

source roles = [Wilson boundary ORIGINAL prime, 79, 11, 14, 154]

derived = [1, 75, 是, 是]

Wilson boundary ORIGINAL prime ORIGINAL running factorial product12 := mul(75, 12)

Wilson boundary ORIGINAL prime ORIGINAL running factorial product12 = 900

source roles = [Wilson boundary ORIGINAL prime, 79, 12, 75, 900]

derived = [11, 31, 是, 是]

Wilson boundary ORIGINAL prime ORIGINAL running factorial product13 := mul(31, 13)

Wilson boundary ORIGINAL prime ORIGINAL running factorial product13 = 403

source roles = [Wilson boundary ORIGINAL prime, 79, 13, 31, 403]

derived = [5, 8, 是, 是]

Wilson boundary ORIGINAL prime ORIGINAL running factorial product14 := mul(8, 14)

Wilson boundary ORIGINAL prime ORIGINAL running factorial product14 = 112

source roles = [Wilson boundary ORIGINAL prime, 79, 14, 8, 112]

derived = [1, 33, 是, 是]

Wilson boundary ORIGINAL prime ORIGINAL running factorial product15 := mul(33, 15)

Wilson boundary ORIGINAL prime ORIGINAL running factorial product15 = 495

source roles = [Wilson boundary ORIGINAL prime, 79, 15, 33, 495]

derived = [6, 21, 是, 是]

Wilson boundary ORIGINAL prime ORIGINAL running factorial product16 := mul(21, 16)

Wilson boundary ORIGINAL prime ORIGINAL running factorial product16 = 336

source roles = [Wilson boundary ORIGINAL prime, 79, 16, 21, 336]

derived = [4, 20, 是, 是]

Wilson boundary ORIGINAL prime ORIGINAL running factorial product17 := mul(20, 17)

Wilson boundary ORIGINAL prime ORIGINAL running factorial product17 = 340

source roles = [Wilson boundary ORIGINAL prime, 79, 17, 20, 340]

derived = [4, 24, 是, 是]

Wilson boundary ORIGINAL prime ORIGINAL running factorial product18 := mul(24, 18)

Wilson boundary ORIGINAL prime ORIGINAL running factorial product18 = 432

source roles = [Wilson boundary ORIGINAL prime, 79, 18, 24, 432]

derived = [5, 37, 是, 是]

Wilson boundary ORIGINAL prime ORIGINAL running factorial product19 := mul(37, 19)

Wilson boundary ORIGINAL prime ORIGINAL running factorial product19 = 703

source roles = [Wilson boundary ORIGINAL prime, 79, 19, 37, 703]

derived = [8, 71, 是, 是]

Wilson boundary ORIGINAL prime ORIGINAL running factorial product20 := mul(71, 20)

Wilson boundary ORIGINAL prime ORIGINAL running factorial product20 = 1420

source roles = [Wilson boundary ORIGINAL prime, 79, 20, 71, 1420]

derived = [17, 77, 是, 是]

Wilson boundary ORIGINAL prime ORIGINAL running factorial product21 := mul(77, 21)

Wilson boundary ORIGINAL prime ORIGINAL running factorial product21 = 1617

source roles = [Wilson boundary ORIGINAL prime, 79, 21, 77, 1617]

derived = [20, 37, 是, 是]

Wilson boundary ORIGINAL prime ORIGINAL running factorial product22 := mul(37, 22)

Wilson boundary ORIGINAL prime ORIGINAL running factorial product22 = 814

source roles = [Wilson boundary ORIGINAL prime, 79, 22, 37, 814]

derived = [10, 24, 是, 是]

Wilson boundary ORIGINAL prime ORIGINAL running factorial product23 := mul(24, 23)

Wilson boundary ORIGINAL prime ORIGINAL running factorial product23 = 552

source roles = [Wilson boundary ORIGINAL prime, 79, 23, 24, 552]

derived = [6, 78, 是, 是]

Wilson boundary ORIGINAL prime ORIGINAL running factorial product24 := mul(78, 24)

Wilson boundary ORIGINAL prime ORIGINAL running factorial product24 = 1872

source roles = [Wilson boundary ORIGINAL prime, 79, 24, 78, 1872]

derived = [23, 55, 是, 是]

Wilson boundary ORIGINAL prime ORIGINAL running factorial product25 := mul(55, 25)

Wilson boundary ORIGINAL prime ORIGINAL running factorial product25 = 1375

source roles = [Wilson boundary ORIGINAL prime, 79, 25, 55, 1375]

derived = [17, 32, 是, 是]

Wilson boundary ORIGINAL prime ORIGINAL running factorial product26 := mul(32, 26)

Wilson boundary ORIGINAL prime ORIGINAL running factorial product26 = 832

source roles = [Wilson boundary ORIGINAL prime, 79, 26, 32, 832]

derived = [10, 42, 是, 是]

Wilson boundary ORIGINAL prime ORIGINAL running factorial product27 := mul(42, 27)

Wilson boundary ORIGINAL prime ORIGINAL running factorial product27 = 1134

source roles = [Wilson boundary ORIGINAL prime, 79, 27, 42, 1134]

derived = [14, 28, 是, 是]

Wilson boundary ORIGINAL prime ORIGINAL running factorial product28 := mul(28, 28)

Wilson boundary ORIGINAL prime ORIGINAL running factorial product28 = 784

source roles = [Wilson boundary ORIGINAL prime, 79, 28, 28, 784]

derived = [9, 73, 是, 是]

Wilson boundary ORIGINAL prime ORIGINAL running factorial product29 := mul(73, 29)

Wilson boundary ORIGINAL prime ORIGINAL running factorial product29 = 2117

source roles = [Wilson boundary ORIGINAL prime, 79, 29, 73, 2117]

derived = [26, 63, 是, 是]

Wilson boundary ORIGINAL prime ORIGINAL running factorial product30 := mul(63, 30)

Wilson boundary ORIGINAL prime ORIGINAL running factorial product30 = 1890

source roles = [Wilson boundary ORIGINAL prime, 79, 30, 63, 1890]

derived = [23, 73, 是, 是]

Wilson boundary ORIGINAL prime ORIGINAL running factorial product31 := mul(73, 31)

Wilson boundary ORIGINAL prime ORIGINAL running factorial product31 = 2263

source roles = [Wilson boundary ORIGINAL prime, 79, 31, 73, 2263]

derived = [28, 51, 是, 是]

Wilson boundary ORIGINAL prime ORIGINAL running factorial product32 := mul(51, 32)

Wilson boundary ORIGINAL prime ORIGINAL running factorial product32 = 1632

source roles = [Wilson boundary ORIGINAL prime, 79, 32, 51, 1632]

derived = [20, 52, 是, 是]

Wilson boundary ORIGINAL prime ORIGINAL running factorial product33 := mul(52, 33)

Wilson boundary ORIGINAL prime ORIGINAL running factorial product33 = 1716

source roles = [Wilson boundary ORIGINAL prime, 79, 33, 52, 1716]

derived = [21, 57, 是, 是]

Wilson boundary ORIGINAL prime ORIGINAL running factorial product34 := mul(57, 34)

Wilson boundary ORIGINAL prime ORIGINAL running factorial product34 = 1938

source roles = [Wilson boundary ORIGINAL prime, 79, 34, 57, 1938]

derived = [24, 42, 是, 是]

Wilson boundary ORIGINAL prime ORIGINAL running factorial product35 := mul(42, 35)

Wilson boundary ORIGINAL prime ORIGINAL running factorial product35 = 1470

source roles = [Wilson boundary ORIGINAL prime, 79, 35, 42, 1470]

derived = [18, 48, 是, 是]

Wilson boundary ORIGINAL prime ORIGINAL running factorial product36 := mul(48, 36)

Wilson boundary ORIGINAL prime ORIGINAL running factorial product36 = 1728

source roles = [Wilson boundary ORIGINAL prime, 79, 36, 48, 1728]

derived = [21, 69, 是, 是]

Wilson boundary ORIGINAL prime ORIGINAL running factorial product37 := mul(69, 37)

Wilson boundary ORIGINAL prime ORIGINAL running factorial product37 = 2553

source roles = [Wilson boundary ORIGINAL prime, 79, 37, 69, 2553]

derived = [32, 25, 是, 是]

Wilson boundary ORIGINAL prime ORIGINAL running factorial product38 := mul(25, 38)

Wilson boundary ORIGINAL prime ORIGINAL running factorial product38 = 950

source roles = [Wilson boundary ORIGINAL prime, 79, 38, 25, 950]

derived = [12, 2, 是, 是]

Wilson boundary ORIGINAL prime ORIGINAL running factorial product39 := mul(2, 39)

Wilson boundary ORIGINAL prime ORIGINAL running factorial product39 = 78

source roles = [Wilson boundary ORIGINAL prime, 79, 39, 2, 78]

derived = [0, 78, 是, 是]

Wilson boundary ORIGINAL prime ORIGINAL running factorial product40 := mul(78, 40)

Wilson boundary ORIGINAL prime ORIGINAL running factorial product40 = 3120

source roles = [Wilson boundary ORIGINAL prime, 79, 40, 78, 3120]

derived = [39, 39, 是, 是]

Wilson boundary ORIGINAL prime ORIGINAL running factorial product41 := mul(39, 41)

Wilson boundary ORIGINAL prime ORIGINAL running factorial product41 = 1599

source roles = [Wilson boundary ORIGINAL prime, 79, 41, 39, 1599]

derived = [20, 19, 是, 是]

Wilson boundary ORIGINAL prime ORIGINAL running factorial product42 := mul(19, 42)

Wilson boundary ORIGINAL prime ORIGINAL running factorial product42 = 798

source roles = [Wilson boundary ORIGINAL prime, 79, 42, 19, 798]

derived = [10, 8, 是, 是]

Wilson boundary ORIGINAL prime ORIGINAL running factorial product43 := mul(8, 43)

Wilson boundary ORIGINAL prime ORIGINAL running factorial product43 = 344

source roles = [Wilson boundary ORIGINAL prime, 79, 43, 8, 344]

derived = [4, 28, 是, 是]

Wilson boundary ORIGINAL prime ORIGINAL running factorial product44 := mul(28, 44)

Wilson boundary ORIGINAL prime ORIGINAL running factorial product44 = 1232

source roles = [Wilson boundary ORIGINAL prime, 79, 44, 28, 1232]

derived = [15, 47, 是, 是]

Wilson boundary ORIGINAL prime ORIGINAL running factorial product45 := mul(47, 45)

Wilson boundary ORIGINAL prime ORIGINAL running factorial product45 = 2115

source roles = [Wilson boundary ORIGINAL prime, 79, 45, 47, 2115]

derived = [26, 61, 是, 是]

Wilson boundary ORIGINAL prime ORIGINAL running factorial product46 := mul(61, 46)

Wilson boundary ORIGINAL prime ORIGINAL running factorial product46 = 2806

source roles = [Wilson boundary ORIGINAL prime, 79, 46, 61, 2806]

derived = [35, 41, 是, 是]

Wilson boundary ORIGINAL prime ORIGINAL running factorial product47 := mul(41, 47)

Wilson boundary ORIGINAL prime ORIGINAL running factorial product47 = 1927

source roles = [Wilson boundary ORIGINAL prime, 79, 47, 41, 1927]

derived = [24, 31, 是, 是]

Wilson boundary ORIGINAL prime ORIGINAL running factorial product48 := mul(31, 48)

Wilson boundary ORIGINAL prime ORIGINAL running factorial product48 = 1488

source roles = [Wilson boundary ORIGINAL prime, 79, 48, 31, 1488]

derived = [18, 66, 是, 是]

Wilson boundary ORIGINAL prime ORIGINAL running factorial product49 := mul(66, 49)

Wilson boundary ORIGINAL prime ORIGINAL running factorial product49 = 3234

source roles = [Wilson boundary ORIGINAL prime, 79, 49, 66, 3234]

derived = [40, 74, 是, 是]

Wilson boundary ORIGINAL prime ORIGINAL running factorial product50 := mul(74, 50)

Wilson boundary ORIGINAL prime ORIGINAL running factorial product50 = 3700

source roles = [Wilson boundary ORIGINAL prime, 79, 50, 74, 3700]

derived = [46, 66, 是, 是]

Wilson boundary ORIGINAL prime ORIGINAL running factorial product51 := mul(66, 51)

Wilson boundary ORIGINAL prime ORIGINAL running factorial product51 = 3366

source roles = [Wilson boundary ORIGINAL prime, 79, 51, 66, 3366]

derived = [42, 48, 是, 是]

Wilson boundary ORIGINAL prime ORIGINAL running factorial product52 := mul(48, 52)

Wilson boundary ORIGINAL prime ORIGINAL running factorial product52 = 2496

source roles = [Wilson boundary ORIGINAL prime, 79, 52, 48, 2496]

derived = [31, 47, 是, 是]

Wilson boundary ORIGINAL prime ORIGINAL running factorial product53 := mul(47, 53)

Wilson boundary ORIGINAL prime ORIGINAL running factorial product53 = 2491

source roles = [Wilson boundary ORIGINAL prime, 79, 53, 47, 2491]

derived = [31, 42, 是, 是]

Wilson boundary ORIGINAL prime ORIGINAL running factorial product54 := mul(42, 54)

Wilson boundary ORIGINAL prime ORIGINAL running factorial product54 = 2268

source roles = [Wilson boundary ORIGINAL prime, 79, 54, 42, 2268]

derived = [28, 56, 是, 是]

Wilson boundary ORIGINAL prime ORIGINAL running factorial product55 := mul(56, 55)

Wilson boundary ORIGINAL prime ORIGINAL running factorial product55 = 3080

source roles = [Wilson boundary ORIGINAL prime, 79, 55, 56, 3080]

derived = [38, 78, 是, 是]

Wilson boundary ORIGINAL prime ORIGINAL running factorial product56 := mul(78, 56)

Wilson boundary ORIGINAL prime ORIGINAL running factorial product56 = 4368

source roles = [Wilson boundary ORIGINAL prime, 79, 56, 78, 4368]

derived = [55, 23, 是, 是]

Wilson boundary ORIGINAL prime ORIGINAL running factorial product57 := mul(23, 57)

Wilson boundary ORIGINAL prime ORIGINAL running factorial product57 = 1311

source roles = [Wilson boundary ORIGINAL prime, 79, 57, 23, 1311]

derived = [16, 47, 是, 是]

Wilson boundary ORIGINAL prime ORIGINAL running factorial product58 := mul(47, 58)

Wilson boundary ORIGINAL prime ORIGINAL running factorial product58 = 2726

source roles = [Wilson boundary ORIGINAL prime, 79, 58, 47, 2726]

derived = [34, 40, 是, 是]

Wilson boundary ORIGINAL prime ORIGINAL running factorial product59 := mul(40, 59)

Wilson boundary ORIGINAL prime ORIGINAL running factorial product59 = 2360

source roles = [Wilson boundary ORIGINAL prime, 79, 59, 40, 2360]

derived = [29, 69, 是, 是]

Wilson boundary ORIGINAL prime ORIGINAL running factorial product60 := mul(69, 60)

Wilson boundary ORIGINAL prime ORIGINAL running factorial product60 = 4140

source roles = [Wilson boundary ORIGINAL prime, 79, 60, 69, 4140]

derived = [52, 32, 是, 是]

Wilson boundary ORIGINAL prime ORIGINAL running factorial product61 := mul(32, 61)

Wilson boundary ORIGINAL prime ORIGINAL running factorial product61 = 1952

source roles = [Wilson boundary ORIGINAL prime, 79, 61, 32, 1952]

derived = [24, 56, 是, 是]

Wilson boundary ORIGINAL prime ORIGINAL running factorial product62 := mul(56, 62)

Wilson boundary ORIGINAL prime ORIGINAL running factorial product62 = 3472

source roles = [Wilson boundary ORIGINAL prime, 79, 62, 56, 3472]

derived = [43, 75, 是, 是]

Wilson boundary ORIGINAL prime ORIGINAL running factorial product63 := mul(75, 63)

Wilson boundary ORIGINAL prime ORIGINAL running factorial product63 = 4725

source roles = [Wilson boundary ORIGINAL prime, 79, 63, 75, 4725]

derived = [59, 64, 是, 是]

Wilson boundary ORIGINAL prime ORIGINAL running factorial product64 := mul(64, 64)

Wilson boundary ORIGINAL prime ORIGINAL running factorial product64 = 4096

source roles = [Wilson boundary ORIGINAL prime, 79, 64, 64, 4096]

derived = [51, 67, 是, 是]

Wilson boundary ORIGINAL prime ORIGINAL running factorial product65 := mul(67, 65)

Wilson boundary ORIGINAL prime ORIGINAL running factorial product65 = 4355

source roles = [Wilson boundary ORIGINAL prime, 79, 65, 67, 4355]

derived = [55, 10, 是, 是]

Wilson boundary ORIGINAL prime ORIGINAL running factorial product66 := mul(10, 66)

Wilson boundary ORIGINAL prime ORIGINAL running factorial product66 = 660

source roles = [Wilson boundary ORIGINAL prime, 79, 66, 10, 660]

derived = [8, 28, 是, 是]

Wilson boundary ORIGINAL prime ORIGINAL running factorial product67 := mul(28, 67)

Wilson boundary ORIGINAL prime ORIGINAL running factorial product67 = 1876

source roles = [Wilson boundary ORIGINAL prime, 79, 67, 28, 1876]

derived = [23, 59, 是, 是]

Wilson boundary ORIGINAL prime ORIGINAL running factorial product68 := mul(59, 68)

Wilson boundary ORIGINAL prime ORIGINAL running factorial product68 = 4012

source roles = [Wilson boundary ORIGINAL prime, 79, 68, 59, 4012]

derived = [50, 62, 是, 是]

Wilson boundary ORIGINAL prime ORIGINAL running factorial product69 := mul(62, 69)

Wilson boundary ORIGINAL prime ORIGINAL running factorial product69 = 4278

source roles = [Wilson boundary ORIGINAL prime, 79, 69, 62, 4278]

derived = [54, 12, 是, 是]

Wilson boundary ORIGINAL prime ORIGINAL running factorial product70 := mul(12, 70)

Wilson boundary ORIGINAL prime ORIGINAL running factorial product70 = 840

source roles = [Wilson boundary ORIGINAL prime, 79, 70, 12, 840]

derived = [10, 50, 是, 是]

Wilson boundary ORIGINAL prime ORIGINAL running factorial product71 := mul(50, 71)

Wilson boundary ORIGINAL prime ORIGINAL running factorial product71 = 3550

source roles = [Wilson boundary ORIGINAL prime, 79, 71, 50, 3550]

derived = [44, 74, 是, 是]

Wilson boundary ORIGINAL prime ORIGINAL running factorial product72 := mul(74, 72)

Wilson boundary ORIGINAL prime ORIGINAL running factorial product72 = 5328

source roles = [Wilson boundary ORIGINAL prime, 79, 72, 74, 5328]

derived = [67, 35, 是, 是]

Wilson boundary ORIGINAL prime ORIGINAL running factorial product73 := mul(35, 73)

Wilson boundary ORIGINAL prime ORIGINAL running factorial product73 = 2555

source roles = [Wilson boundary ORIGINAL prime, 79, 73, 35, 2555]

derived = [32, 27, 是, 是]

Wilson boundary ORIGINAL prime ORIGINAL running factorial product74 := mul(27, 74)

Wilson boundary ORIGINAL prime ORIGINAL running factorial product74 = 1998

source roles = [Wilson boundary ORIGINAL prime, 79, 74, 27, 1998]

derived = [25, 23, 是, 是]

Wilson boundary ORIGINAL prime ORIGINAL running factorial product75 := mul(23, 75)

Wilson boundary ORIGINAL prime ORIGINAL running factorial product75 = 1725

source roles = [Wilson boundary ORIGINAL prime, 79, 75, 23, 1725]

derived = [21, 66, 是, 是]

Wilson boundary ORIGINAL prime ORIGINAL running factorial product76 := mul(66, 76)

Wilson boundary ORIGINAL prime ORIGINAL running factorial product76 = 5016

source roles = [Wilson boundary ORIGINAL prime, 79, 76, 66, 5016]

derived = [63, 39, 是, 是]

Wilson boundary ORIGINAL prime ORIGINAL running factorial product77 := mul(39, 77)

Wilson boundary ORIGINAL prime ORIGINAL running factorial product77 = 3003

source roles = [Wilson boundary ORIGINAL prime, 79, 77, 39, 3003]

derived = [38, 1, 是, 是]

Wilson boundary ORIGINAL prime ORIGINAL running factorial product78 := mul(1, 78)

Wilson boundary ORIGINAL prime ORIGINAL running factorial product78 = 78

source roles = [Wilson boundary ORIGINAL prime, 79, 78, 1, 78]

derived = [0, 78, 是, 是]

source roles = [79, [[1, 1], [2, 2], [3, 6], [4, 24], [5, 41], [6, 9], [7, 63], [8, 30], [9, 33], [10, 14], [11, 75], [12, 31], [13, 8], [14, 33], [15, 21], [16, 20], [17, 24], [18, 37], [19, 71], [20, 77], [21, 37], [22, 24], [23, 78], [24, 55], [25, 32], [26, 42], [27, 28], [28, 73], [29, 63], [30, 73], [31, 51], [32, 52], [33, 57], [34, 42], [35, 48], [36, 69], [37, 25], [38, 2], [39, 78], [40, 39], [41, 19], [42, 8], [43, 28], [44, 47], [45, 61], [46, 41], [47, 31], [48, 66], [49, 74], [50, 66], [51, 48], [52, 47], [53, 42], [54, 56], [55, 78], [56, 23], [57, 47], [58, 40], [59, 69], [60, 32], [61, 56], [62, 75], [63, 64], [64, 67], [65, 10], [66, 28], [67, 59], [68, 62], [69, 12], [70, 50], [71, 74], [72, 35], [73, 27], [74, 23], [75, 66], [76, 39], [77, 1], [78, 78]], 78]

derived = [78, 是, 否]

逐步反向核對

• S158 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S157 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S156 · premise_and_result_audit — 以精確有理數重算 Wilson boundary ORIGINAL prime ORIGINAL running factorial product78，不以小數近似替代。
• S155 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S154 · premise_and_result_audit — 以精確有理數重算 Wilson boundary ORIGINAL prime ORIGINAL running factorial product77，不以小數近似替代。
• S153 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S152 · premise_and_result_audit — 以精確有理數重算 Wilson boundary ORIGINAL prime ORIGINAL running factorial product76，不以小數近似替代。
• S151 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S150 · premise_and_result_audit — 以精確有理數重算 Wilson boundary ORIGINAL prime ORIGINAL running factorial product75，不以小數近似替代。
• S149 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S148 · premise_and_result_audit — 以精確有理數重算 Wilson boundary ORIGINAL prime ORIGINAL running factorial product74，不以小數近似替代。
• S147 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S146 · premise_and_result_audit — 以精確有理數重算 Wilson boundary ORIGINAL prime ORIGINAL running factorial product73，不以小數近似替代。
• S145 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S144 · premise_and_result_audit — 以精確有理數重算 Wilson boundary ORIGINAL prime ORIGINAL running factorial product72，不以小數近似替代。
• S143 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S142 · premise_and_result_audit — 以精確有理數重算 Wilson boundary ORIGINAL prime ORIGINAL running factorial product71，不以小數近似替代。
• S141 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S140 · premise_and_result_audit — 以精確有理數重算 Wilson boundary ORIGINAL prime ORIGINAL running factorial product70，不以小數近似替代。
• S139 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S138 · premise_and_result_audit — 以精確有理數重算 Wilson boundary ORIGINAL prime ORIGINAL running factorial product69，不以小數近似替代。
• S137 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S136 · premise_and_result_audit — 以精確有理數重算 Wilson boundary ORIGINAL prime ORIGINAL running factorial product68，不以小數近似替代。
• S135 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S134 · premise_and_result_audit — 以精確有理數重算 Wilson boundary ORIGINAL prime ORIGINAL running factorial product67，不以小數近似替代。
• S133 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S132 · premise_and_result_audit — 以精確有理數重算 Wilson boundary ORIGINAL prime ORIGINAL running factorial product66，不以小數近似替代。
• S131 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S130 · premise_and_result_audit — 以精確有理數重算 Wilson boundary ORIGINAL prime ORIGINAL running factorial product65，不以小數近似替代。
• S129 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S128 · premise_and_result_audit — 以精確有理數重算 Wilson boundary ORIGINAL prime ORIGINAL running factorial product64，不以小數近似替代。
• S127 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S126 · premise_and_result_audit — 以精確有理數重算 Wilson boundary ORIGINAL prime ORIGINAL running factorial product63，不以小數近似替代。
• S125 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S124 · premise_and_result_audit — 以精確有理數重算 Wilson boundary ORIGINAL prime ORIGINAL running factorial product62，不以小數近似替代。
• S123 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S122 · premise_and_result_audit — 以精確有理數重算 Wilson boundary ORIGINAL prime ORIGINAL running factorial product61，不以小數近似替代。
• S121 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S120 · premise_and_result_audit — 以精確有理數重算 Wilson boundary ORIGINAL prime ORIGINAL running factorial product60，不以小數近似替代。
• S119 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S118 · premise_and_result_audit — 以精確有理數重算 Wilson boundary ORIGINAL prime ORIGINAL running factorial product59，不以小數近似替代。
• S117 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S116 · premise_and_result_audit — 以精確有理數重算 Wilson boundary ORIGINAL prime ORIGINAL running factorial product58，不以小數近似替代。
• S115 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S114 · premise_and_result_audit — 以精確有理數重算 Wilson boundary ORIGINAL prime ORIGINAL running factorial product57，不以小數近似替代。
• S113 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S112 · premise_and_result_audit — 以精確有理數重算 Wilson boundary ORIGINAL prime ORIGINAL running factorial product56，不以小數近似替代。
• S111 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S110 · premise_and_result_audit — 以精確有理數重算 Wilson boundary ORIGINAL prime ORIGINAL running factorial product55，不以小數近似替代。
• S109 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S108 · premise_and_result_audit — 以精確有理數重算 Wilson boundary ORIGINAL prime ORIGINAL running factorial product54，不以小數近似替代。
• S107 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S106 · premise_and_result_audit — 以精確有理數重算 Wilson boundary ORIGINAL prime ORIGINAL running factorial product53，不以小數近似替代。
• S105 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S104 · premise_and_result_audit — 以精確有理數重算 Wilson boundary ORIGINAL prime ORIGINAL running factorial product52，不以小數近似替代。
• S103 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S102 · premise_and_result_audit — 以精確有理數重算 Wilson boundary ORIGINAL prime ORIGINAL running factorial product51，不以小數近似替代。
• S101 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S100 · premise_and_result_audit — 以精確有理數重算 Wilson boundary ORIGINAL prime ORIGINAL running factorial product50，不以小數近似替代。
• S099 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S098 · premise_and_result_audit — 以精確有理數重算 Wilson boundary ORIGINAL prime ORIGINAL running factorial product49，不以小數近似替代。
• S097 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S096 · premise_and_result_audit — 以精確有理數重算 Wilson boundary ORIGINAL prime ORIGINAL running factorial product48，不以小數近似替代。
• S095 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S094 · premise_and_result_audit — 以精確有理數重算 Wilson boundary ORIGINAL prime ORIGINAL running factorial product47，不以小數近似替代。
• S093 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S092 · premise_and_result_audit — 以精確有理數重算 Wilson boundary ORIGINAL prime ORIGINAL running factorial product46，不以小數近似替代。
• S091 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S090 · premise_and_result_audit — 以精確有理數重算 Wilson boundary ORIGINAL prime ORIGINAL running factorial product45，不以小數近似替代。
• S089 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S088 · premise_and_result_audit — 以精確有理數重算 Wilson boundary ORIGINAL prime ORIGINAL running factorial product44，不以小數近似替代。
• S087 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S086 · premise_and_result_audit — 以精確有理數重算 Wilson boundary ORIGINAL prime ORIGINAL running factorial product43，不以小數近似替代。
• S085 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S084 · premise_and_result_audit — 以精確有理數重算 Wilson boundary ORIGINAL prime ORIGINAL running factorial product42，不以小數近似替代。
• S083 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S082 · premise_and_result_audit — 以精確有理數重算 Wilson boundary ORIGINAL prime ORIGINAL running factorial product41，不以小數近似替代。
• S081 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S080 · premise_and_result_audit — 以精確有理數重算 Wilson boundary ORIGINAL prime ORIGINAL running factorial product40，不以小數近似替代。
• S079 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S078 · premise_and_result_audit — 以精確有理數重算 Wilson boundary ORIGINAL prime ORIGINAL running factorial product39，不以小數近似替代。
• S077 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S076 · premise_and_result_audit — 以精確有理數重算 Wilson boundary ORIGINAL prime ORIGINAL running factorial product38，不以小數近似替代。
• S075 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S074 · premise_and_result_audit — 以精確有理數重算 Wilson boundary ORIGINAL prime ORIGINAL running factorial product37，不以小數近似替代。
• S073 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S072 · premise_and_result_audit — 以精確有理數重算 Wilson boundary ORIGINAL prime ORIGINAL running factorial product36，不以小數近似替代。
• S071 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S070 · premise_and_result_audit — 以精確有理數重算 Wilson boundary ORIGINAL prime ORIGINAL running factorial product35，不以小數近似替代。
• S069 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S068 · premise_and_result_audit — 以精確有理數重算 Wilson boundary ORIGINAL prime ORIGINAL running factorial product34，不以小數近似替代。
• S067 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S066 · premise_and_result_audit — 以精確有理數重算 Wilson boundary ORIGINAL prime ORIGINAL running factorial product33，不以小數近似替代。
• S065 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S064 · premise_and_result_audit — 以精確有理數重算 Wilson boundary ORIGINAL prime ORIGINAL running factorial product32，不以小數近似替代。
• S063 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S062 · premise_and_result_audit — 以精確有理數重算 Wilson boundary ORIGINAL prime ORIGINAL running factorial product31，不以小數近似替代。
• S061 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S060 · premise_and_result_audit — 以精確有理數重算 Wilson boundary ORIGINAL prime ORIGINAL running factorial product30，不以小數近似替代。
• S059 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S058 · premise_and_result_audit — 以精確有理數重算 Wilson boundary ORIGINAL prime ORIGINAL running factorial product29，不以小數近似替代。
• S057 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S056 · premise_and_result_audit — 以精確有理數重算 Wilson boundary ORIGINAL prime ORIGINAL running factorial product28，不以小數近似替代。
• S055 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S054 · premise_and_result_audit — 以精確有理數重算 Wilson boundary ORIGINAL prime ORIGINAL running factorial product27，不以小數近似替代。
• S053 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S052 · premise_and_result_audit — 以精確有理數重算 Wilson boundary ORIGINAL prime ORIGINAL running factorial product26，不以小數近似替代。
• S051 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S050 · premise_and_result_audit — 以精確有理數重算 Wilson boundary ORIGINAL prime ORIGINAL running factorial product25，不以小數近似替代。
• S049 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S048 · premise_and_result_audit — 以精確有理數重算 Wilson boundary ORIGINAL prime ORIGINAL running factorial product24，不以小數近似替代。
• S047 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S046 · premise_and_result_audit — 以精確有理數重算 Wilson boundary ORIGINAL prime ORIGINAL running factorial product23，不以小數近似替代。
• S045 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S044 · premise_and_result_audit — 以精確有理數重算 Wilson boundary ORIGINAL prime ORIGINAL running factorial product22，不以小數近似替代。
• S043 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S042 · premise_and_result_audit — 以精確有理數重算 Wilson boundary ORIGINAL prime ORIGINAL running factorial product21，不以小數近似替代。
• S041 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S040 · premise_and_result_audit — 以精確有理數重算 Wilson boundary ORIGINAL prime ORIGINAL running factorial product20，不以小數近似替代。
• S039 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S038 · premise_and_result_audit — 以精確有理數重算 Wilson boundary ORIGINAL prime ORIGINAL running factorial product19，不以小數近似替代。
• S037 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S036 · premise_and_result_audit — 以精確有理數重算 Wilson boundary ORIGINAL prime ORIGINAL running factorial product18，不以小數近似替代。
• S035 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S034 · premise_and_result_audit — 以精確有理數重算 Wilson boundary ORIGINAL prime ORIGINAL running factorial product17，不以小數近似替代。
• S033 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S032 · premise_and_result_audit — 以精確有理數重算 Wilson boundary ORIGINAL prime ORIGINAL running factorial product16，不以小數近似替代。
• S031 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S030 · premise_and_result_audit — 以精確有理數重算 Wilson boundary ORIGINAL prime ORIGINAL running factorial product15，不以小數近似替代。
• S029 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S028 · premise_and_result_audit — 以精確有理數重算 Wilson boundary ORIGINAL prime ORIGINAL running factorial product14，不以小數近似替代。
• S027 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S026 · premise_and_result_audit — 以精確有理數重算 Wilson boundary ORIGINAL prime ORIGINAL running factorial product13，不以小數近似替代。
• S025 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S024 · premise_and_result_audit — 以精確有理數重算 Wilson boundary ORIGINAL prime ORIGINAL running factorial product12，不以小數近似替代。
• S023 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S022 · premise_and_result_audit — 以精確有理數重算 Wilson boundary ORIGINAL prime ORIGINAL running factorial product11，不以小數近似替代。
• S021 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S020 · premise_and_result_audit — 以精確有理數重算 Wilson boundary ORIGINAL prime ORIGINAL running factorial product10，不以小數近似替代。
• S019 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S018 · premise_and_result_audit — 以精確有理數重算 Wilson boundary ORIGINAL prime ORIGINAL running factorial product9，不以小數近似替代。
• S017 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S016 · premise_and_result_audit — 以精確有理數重算 Wilson boundary ORIGINAL prime ORIGINAL running factorial product8，不以小數近似替代。
• S015 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S014 · premise_and_result_audit — 以精確有理數重算 Wilson boundary ORIGINAL prime ORIGINAL running factorial product7，不以小數近似替代。
• S013 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S012 · premise_and_result_audit — 以精確有理數重算 Wilson boundary ORIGINAL prime ORIGINAL running factorial product6，不以小數近似替代。
• S011 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S010 · premise_and_result_audit — 以精確有理數重算 Wilson boundary ORIGINAL prime ORIGINAL running factorial product5，不以小數近似替代。
• S009 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S008 · premise_and_result_audit — 以精確有理數重算 Wilson boundary ORIGINAL prime ORIGINAL running factorial product4，不以小數近似替代。
• S007 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S006 · premise_and_result_audit — 以精確有理數重算 Wilson boundary ORIGINAL prime ORIGINAL running factorial product3，不以小數近似替代。
• S005 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S004 · premise_and_result_audit — 以精確有理數重算 Wilson boundary ORIGINAL prime ORIGINAL running factorial product2，不以小數近似替代。
• S003 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S002 · premise_and_result_audit — 以精確有理數重算 Wilson boundary ORIGINAL prime ORIGINAL running factorial product1，不以小數近似替代。
• S001 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。

結論

(fermat_confusion, 79, [[1, 1], [2, 2], [3, 6], [4, 24], [5, 41], [6, 9], [7, 63], [8, 30], [9, 33], [10, 14], [11, 75], [12, 31], [13, 8], [14, 33], [15, 21], [16, 20], [17, 24], [18, 37], [19, 71], [20, 77], [21, 37], [22, 24], [23, 78], [24, 55], [25, 32], [26, 42], [27, 28], [28, 73], [29, 63], [30, 73], [31, 51], [32, 52], [33, 57], [34, 42], [35, 48], [36, 69], [37, 25], [38, 2], [39, 78], [40, 39], [41, 19], [42, 8], [43, 28], [44, 47], [45, 61], [46, 41], [47, 31], [48, 66], [49, 74], [50, 66], [51, 48], [52, 47], [53, 42], [54, 56], [55, 78], [56, 23], [57, 47], [58, 40], [59, 69], [60, 32], [61, 56], [62, 75], [63, 64], [64, 67], [65, 10], [66, 28], [67, 59], [68, 62], [69, 12], [70, 50], [71, 74], [72, 35], [73, 27], [74, 23], [75, 66], [76, 39], [77, 1], [78, 78]], 78, 78, 是, Wilson:(n-1)!==-1_mod_79, Fermat:a^(79-1)==1_mod_79_when_n_does_not_divide_a, 否, distinct_theorems_no_Fermat_power_claim_recomputed)

依上列完整代值及條件核對得到原題答案；原題編號、格式與狀態保持不變。

本題覆核與來源綁定

覆核日期：2026-10-26

原題、答案、步驟表達式、數值 AST 與既有歷史保持原樣；原來的候選狀態屬於來源歷史，不覆寫為形式化證明。