第 27795 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-prime-inverse-pairing；資料={"p":71}。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-prime-inverse-pairing；資料={"p":71}。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-prime-inverse-pairing]

derived = [[p, all_inverse_pairs, self_inverse_residues, distinct_cancelling_pairs, self_inverse_scope, factorial_residue, Wilson_congruence]]

source roles = [71, 1]

derived = [1, 1]

source roles = [71, 2]

derived = [36, 1]

source roles = [71, 3]

derived = [24, 1]

source roles = [71, 4]

derived = [18, 1]

source roles = [71, 5]

derived = [57, 1]

source roles = [71, 6]

derived = [12, 1]

source roles = [71, 7]

derived = [61, 1]

source roles = [71, 8]

derived = [9, 1]

source roles = [71, 9]

derived = [8, 1]

source roles = [71, 10]

derived = [64, 1]

source roles = [71, 11]

derived = [13, 1]

source roles = [71, 12]

derived = [6, 1]

source roles = [71, 13]

derived = [11, 1]

source roles = [71, 14]

derived = [66, 1]

source roles = [71, 15]

derived = [19, 1]

source roles = [71, 16]

derived = [40, 1]

source roles = [71, 17]

derived = [46, 1]

source roles = [71, 18]

derived = [4, 1]

source roles = [71, 19]

derived = [15, 1]

source roles = [71, 20]

derived = [32, 1]

source roles = [71, 21]

derived = [44, 1]

source roles = [71, 22]

derived = [42, 1]

source roles = [71, 23]

derived = [34, 1]

source roles = [71, 24]

derived = [3, 1]

source roles = [71, 25]

derived = [54, 1]

source roles = [71, 26]

derived = [41, 1]

source roles = [71, 27]

derived = [50, 1]

source roles = [71, 28]

derived = [33, 1]

source roles = [71, 29]

derived = [49, 1]

source roles = [71, 30]

derived = [45, 1]

source roles = [71, 31]

derived = [55, 1]

source roles = [71, 32]

derived = [20, 1]

source roles = [71, 33]

derived = [28, 1]

source roles = [71, 34]

derived = [23, 1]

source roles = [71, 35]

derived = [69, 1]

source roles = [71, 36]

derived = [2, 1]

source roles = [71, 37]

derived = [48, 1]

source roles = [71, 38]

derived = [43, 1]

source roles = [71, 39]

derived = [51, 1]

source roles = [71, 40]

derived = [16, 1]

source roles = [71, 41]

derived = [26, 1]

source roles = [71, 42]

derived = [22, 1]

source roles = [71, 43]

derived = [38, 1]

source roles = [71, 44]

derived = [21, 1]

source roles = [71, 45]

derived = [30, 1]

source roles = [71, 46]

derived = [17, 1]

source roles = [71, 47]

derived = [68, 1]

source roles = [71, 48]

derived = [37, 1]

source roles = [71, 49]

derived = [29, 1]

source roles = [71, 50]

derived = [27, 1]

source roles = [71, 51]

derived = [39, 1]

source roles = [71, 52]

derived = [56, 1]

source roles = [71, 53]

derived = [67, 1]

source roles = [71, 54]

derived = [25, 1]

source roles = [71, 55]

derived = [31, 1]

source roles = [71, 56]

derived = [52, 1]

source roles = [71, 57]

derived = [5, 1]

source roles = [71, 58]

derived = [60, 1]

source roles = [71, 59]

derived = [65, 1]

source roles = [71, 60]

derived = [58, 1]

source roles = [71, 61]

derived = [7, 1]

source roles = [71, 62]

derived = [63, 1]

source roles = [71, 63]

derived = [62, 1]

source roles = [71, 64]

derived = [10, 1]

source roles = [71, 65]

derived = [59, 1]

source roles = [71, 66]

derived = [14, 1]

source roles = [71, 67]

derived = [53, 1]

source roles = [71, 68]

derived = [47, 1]

source roles = [71, 69]

derived = [35, 1]

source roles = [71, 70]

derived = [70, 1]

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

Wilson ORIGINAL prime factorial ORIGINAL running factorial product1 = 1

source roles = [Wilson ORIGINAL prime factorial, 71, 1, 1, 1]

derived = [0, 1, 是, 是]

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

Wilson ORIGINAL prime factorial ORIGINAL running factorial product2 = 2

source roles = [Wilson ORIGINAL prime factorial, 71, 2, 1, 2]

derived = [0, 2, 是, 是]

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

Wilson ORIGINAL prime factorial ORIGINAL running factorial product3 = 6

source roles = [Wilson ORIGINAL prime factorial, 71, 3, 2, 6]

derived = [0, 6, 是, 是]

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

Wilson ORIGINAL prime factorial ORIGINAL running factorial product4 = 24

source roles = [Wilson ORIGINAL prime factorial, 71, 4, 6, 24]

derived = [0, 24, 是, 是]

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

Wilson ORIGINAL prime factorial ORIGINAL running factorial product5 = 120

source roles = [Wilson ORIGINAL prime factorial, 71, 5, 24, 120]

derived = [1, 49, 是, 是]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product6 := mul(49, 6)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product6 = 294

source roles = [Wilson ORIGINAL prime factorial, 71, 6, 49, 294]

derived = [4, 10, 是, 是]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product7 := mul(10, 7)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product7 = 70

source roles = [Wilson ORIGINAL prime factorial, 71, 7, 10, 70]

derived = [0, 70, 是, 是]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product8 := mul(70, 8)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product8 = 560

source roles = [Wilson ORIGINAL prime factorial, 71, 8, 70, 560]

derived = [7, 63, 是, 是]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product9 := mul(63, 9)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product9 = 567

source roles = [Wilson ORIGINAL prime factorial, 71, 9, 63, 567]

derived = [7, 70, 是, 是]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product10 := mul(70, 10)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product10 = 700

source roles = [Wilson ORIGINAL prime factorial, 71, 10, 70, 700]

derived = [9, 61, 是, 是]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product11 := mul(61, 11)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product11 = 671

source roles = [Wilson ORIGINAL prime factorial, 71, 11, 61, 671]

derived = [9, 32, 是, 是]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product12 := mul(32, 12)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product12 = 384

source roles = [Wilson ORIGINAL prime factorial, 71, 12, 32, 384]

derived = [5, 29, 是, 是]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product13 := mul(29, 13)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product13 = 377

source roles = [Wilson ORIGINAL prime factorial, 71, 13, 29, 377]

derived = [5, 22, 是, 是]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product14 := mul(22, 14)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product14 = 308

source roles = [Wilson ORIGINAL prime factorial, 71, 14, 22, 308]

derived = [4, 24, 是, 是]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product15 := mul(24, 15)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product15 = 360

source roles = [Wilson ORIGINAL prime factorial, 71, 15, 24, 360]

derived = [5, 5, 是, 是]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product16 := mul(5, 16)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product16 = 80

source roles = [Wilson ORIGINAL prime factorial, 71, 16, 5, 80]

derived = [1, 9, 是, 是]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product17 := mul(9, 17)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product17 = 153

source roles = [Wilson ORIGINAL prime factorial, 71, 17, 9, 153]

derived = [2, 11, 是, 是]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product18 := mul(11, 18)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product18 = 198

source roles = [Wilson ORIGINAL prime factorial, 71, 18, 11, 198]

derived = [2, 56, 是, 是]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product19 := mul(56, 19)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product19 = 1064

source roles = [Wilson ORIGINAL prime factorial, 71, 19, 56, 1064]

derived = [14, 70, 是, 是]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product20 := mul(70, 20)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product20 = 1400

source roles = [Wilson ORIGINAL prime factorial, 71, 20, 70, 1400]

derived = [19, 51, 是, 是]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product21 := mul(51, 21)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product21 = 1071

source roles = [Wilson ORIGINAL prime factorial, 71, 21, 51, 1071]

derived = [15, 6, 是, 是]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product22 := mul(6, 22)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product22 = 132

source roles = [Wilson ORIGINAL prime factorial, 71, 22, 6, 132]

derived = [1, 61, 是, 是]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product23 := mul(61, 23)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product23 = 1403

source roles = [Wilson ORIGINAL prime factorial, 71, 23, 61, 1403]

derived = [19, 54, 是, 是]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product24 := mul(54, 24)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product24 = 1296

source roles = [Wilson ORIGINAL prime factorial, 71, 24, 54, 1296]

derived = [18, 18, 是, 是]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product25 := mul(18, 25)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product25 = 450

source roles = [Wilson ORIGINAL prime factorial, 71, 25, 18, 450]

derived = [6, 24, 是, 是]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product26 := mul(24, 26)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product26 = 624

source roles = [Wilson ORIGINAL prime factorial, 71, 26, 24, 624]

derived = [8, 56, 是, 是]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product27 := mul(56, 27)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product27 = 1512

source roles = [Wilson ORIGINAL prime factorial, 71, 27, 56, 1512]

derived = [21, 21, 是, 是]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product28 := mul(21, 28)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product28 = 588

source roles = [Wilson ORIGINAL prime factorial, 71, 28, 21, 588]

derived = [8, 20, 是, 是]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product29 := mul(20, 29)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product29 = 580

source roles = [Wilson ORIGINAL prime factorial, 71, 29, 20, 580]

derived = [8, 12, 是, 是]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product30 := mul(12, 30)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product30 = 360

source roles = [Wilson ORIGINAL prime factorial, 71, 30, 12, 360]

derived = [5, 5, 是, 是]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product31 := mul(5, 31)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product31 = 155

source roles = [Wilson ORIGINAL prime factorial, 71, 31, 5, 155]

derived = [2, 13, 是, 是]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product32 := mul(13, 32)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product32 = 416

source roles = [Wilson ORIGINAL prime factorial, 71, 32, 13, 416]

derived = [5, 61, 是, 是]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product33 := mul(61, 33)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product33 = 2013

source roles = [Wilson ORIGINAL prime factorial, 71, 33, 61, 2013]

derived = [28, 25, 是, 是]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product34 := mul(25, 34)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product34 = 850

source roles = [Wilson ORIGINAL prime factorial, 71, 34, 25, 850]

derived = [11, 69, 是, 是]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product35 := mul(69, 35)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product35 = 2415

source roles = [Wilson ORIGINAL prime factorial, 71, 35, 69, 2415]

derived = [34, 1, 是, 是]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product36 := mul(1, 36)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product36 = 36

source roles = [Wilson ORIGINAL prime factorial, 71, 36, 1, 36]

derived = [0, 36, 是, 是]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product37 := mul(36, 37)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product37 = 1332

source roles = [Wilson ORIGINAL prime factorial, 71, 37, 36, 1332]

derived = [18, 54, 是, 是]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product38 := mul(54, 38)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product38 = 2052

source roles = [Wilson ORIGINAL prime factorial, 71, 38, 54, 2052]

derived = [28, 64, 是, 是]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product39 := mul(64, 39)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product39 = 2496

source roles = [Wilson ORIGINAL prime factorial, 71, 39, 64, 2496]

derived = [35, 11, 是, 是]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product40 := mul(11, 40)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product40 = 440

source roles = [Wilson ORIGINAL prime factorial, 71, 40, 11, 440]

derived = [6, 14, 是, 是]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product41 := mul(14, 41)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product41 = 574

source roles = [Wilson ORIGINAL prime factorial, 71, 41, 14, 574]

derived = [8, 6, 是, 是]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product42 := mul(6, 42)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product42 = 252

source roles = [Wilson ORIGINAL prime factorial, 71, 42, 6, 252]

derived = [3, 39, 是, 是]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product43 := mul(39, 43)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product43 = 1677

source roles = [Wilson ORIGINAL prime factorial, 71, 43, 39, 1677]

derived = [23, 44, 是, 是]

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

Wilson ORIGINAL prime factorial ORIGINAL running factorial product44 = 1936

source roles = [Wilson ORIGINAL prime factorial, 71, 44, 44, 1936]

derived = [27, 19, 是, 是]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product45 := mul(19, 45)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product45 = 855

source roles = [Wilson ORIGINAL prime factorial, 71, 45, 19, 855]

derived = [12, 3, 是, 是]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product46 := mul(3, 46)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product46 = 138

source roles = [Wilson ORIGINAL prime factorial, 71, 46, 3, 138]

derived = [1, 67, 是, 是]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product47 := mul(67, 47)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product47 = 3149

source roles = [Wilson ORIGINAL prime factorial, 71, 47, 67, 3149]

derived = [44, 25, 是, 是]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product48 := mul(25, 48)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product48 = 1200

source roles = [Wilson ORIGINAL prime factorial, 71, 48, 25, 1200]

derived = [16, 64, 是, 是]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product49 := mul(64, 49)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product49 = 3136

source roles = [Wilson ORIGINAL prime factorial, 71, 49, 64, 3136]

derived = [44, 12, 是, 是]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product50 := mul(12, 50)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product50 = 600

source roles = [Wilson ORIGINAL prime factorial, 71, 50, 12, 600]

derived = [8, 32, 是, 是]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product51 := mul(32, 51)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product51 = 1632

source roles = [Wilson ORIGINAL prime factorial, 71, 51, 32, 1632]

derived = [22, 70, 是, 是]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product52 := mul(70, 52)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product52 = 3640

source roles = [Wilson ORIGINAL prime factorial, 71, 52, 70, 3640]

derived = [51, 19, 是, 是]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product53 := mul(19, 53)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product53 = 1007

source roles = [Wilson ORIGINAL prime factorial, 71, 53, 19, 1007]

derived = [14, 13, 是, 是]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product54 := mul(13, 54)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product54 = 702

source roles = [Wilson ORIGINAL prime factorial, 71, 54, 13, 702]

derived = [9, 63, 是, 是]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product55 := mul(63, 55)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product55 = 3465

source roles = [Wilson ORIGINAL prime factorial, 71, 55, 63, 3465]

derived = [48, 57, 是, 是]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product56 := mul(57, 56)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product56 = 3192

source roles = [Wilson ORIGINAL prime factorial, 71, 56, 57, 3192]

derived = [44, 68, 是, 是]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product57 := mul(68, 57)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product57 = 3876

source roles = [Wilson ORIGINAL prime factorial, 71, 57, 68, 3876]

derived = [54, 42, 是, 是]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product58 := mul(42, 58)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product58 = 2436

source roles = [Wilson ORIGINAL prime factorial, 71, 58, 42, 2436]

derived = [34, 22, 是, 是]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product59 := mul(22, 59)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product59 = 1298

source roles = [Wilson ORIGINAL prime factorial, 71, 59, 22, 1298]

derived = [18, 20, 是, 是]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product60 := mul(20, 60)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product60 = 1200

source roles = [Wilson ORIGINAL prime factorial, 71, 60, 20, 1200]

derived = [16, 64, 是, 是]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product61 := mul(64, 61)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product61 = 3904

source roles = [Wilson ORIGINAL prime factorial, 71, 61, 64, 3904]

derived = [54, 70, 是, 是]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product62 := mul(70, 62)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product62 = 4340

source roles = [Wilson ORIGINAL prime factorial, 71, 62, 70, 4340]

derived = [61, 9, 是, 是]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product63 := mul(9, 63)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product63 = 567

source roles = [Wilson ORIGINAL prime factorial, 71, 63, 9, 567]

derived = [7, 70, 是, 是]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product64 := mul(70, 64)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product64 = 4480

source roles = [Wilson ORIGINAL prime factorial, 71, 64, 70, 4480]

derived = [63, 7, 是, 是]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product65 := mul(7, 65)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product65 = 455

source roles = [Wilson ORIGINAL prime factorial, 71, 65, 7, 455]

derived = [6, 29, 是, 是]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product66 := mul(29, 66)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product66 = 1914

source roles = [Wilson ORIGINAL prime factorial, 71, 66, 29, 1914]

derived = [26, 68, 是, 是]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product67 := mul(68, 67)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product67 = 4556

source roles = [Wilson ORIGINAL prime factorial, 71, 67, 68, 4556]

derived = [64, 12, 是, 是]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product68 := mul(12, 68)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product68 = 816

source roles = [Wilson ORIGINAL prime factorial, 71, 68, 12, 816]

derived = [11, 35, 是, 是]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product69 := mul(35, 69)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product69 = 2415

source roles = [Wilson ORIGINAL prime factorial, 71, 69, 35, 2415]

derived = [34, 1, 是, 是]

Wilson ORIGINAL prime factorial ORIGINAL running factorial product70 := mul(1, 70)

Wilson ORIGINAL prime factorial ORIGINAL running factorial product70 = 70

source roles = [Wilson ORIGINAL prime factorial, 71, 70, 1, 70]

derived = [0, 70, 是, 是]

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

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

逐步反向核對

• S212 · 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。
• S211 · 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。
• S210 · premise_and_result_audit — 以精確有理數重算 Wilson ORIGINAL prime factorial ORIGINAL running factorial product70，不以小數近似替代。
• S209 · 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。
• S208 · premise_and_result_audit — 以精確有理數重算 Wilson ORIGINAL prime factorial ORIGINAL running factorial product69，不以小數近似替代。
• S207 · 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。
• S206 · premise_and_result_audit — 以精確有理數重算 Wilson ORIGINAL prime factorial ORIGINAL running factorial product68，不以小數近似替代。
• S205 · 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。
• S204 · premise_and_result_audit — 以精確有理數重算 Wilson ORIGINAL prime factorial ORIGINAL running factorial product67，不以小數近似替代。
• S203 · 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。
• S202 · premise_and_result_audit — 以精確有理數重算 Wilson ORIGINAL prime factorial ORIGINAL running factorial product66，不以小數近似替代。
• S201 · 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。
• S200 · premise_and_result_audit — 以精確有理數重算 Wilson ORIGINAL prime factorial ORIGINAL running factorial product65，不以小數近似替代。
• S199 · 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。
• S198 · premise_and_result_audit — 以精確有理數重算 Wilson ORIGINAL prime factorial ORIGINAL running factorial product64，不以小數近似替代。
• S197 · 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。
• S196 · premise_and_result_audit — 以精確有理數重算 Wilson ORIGINAL prime factorial ORIGINAL running factorial product63，不以小數近似替代。
• S195 · 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。
• S194 · premise_and_result_audit — 以精確有理數重算 Wilson ORIGINAL prime factorial ORIGINAL running factorial product62，不以小數近似替代。
• S193 · 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。
• S192 · premise_and_result_audit — 以精確有理數重算 Wilson ORIGINAL prime factorial ORIGINAL running factorial product61，不以小數近似替代。
• S191 · 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。
• S190 · premise_and_result_audit — 以精確有理數重算 Wilson ORIGINAL prime factorial ORIGINAL running factorial product60，不以小數近似替代。
• S189 · 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。
• S188 · premise_and_result_audit — 以精確有理數重算 Wilson ORIGINAL prime factorial ORIGINAL running factorial product59，不以小數近似替代。
• S187 · 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。
• S186 · premise_and_result_audit — 以精確有理數重算 Wilson ORIGINAL prime factorial ORIGINAL running factorial product58，不以小數近似替代。
• S185 · 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。
• S184 · premise_and_result_audit — 以精確有理數重算 Wilson ORIGINAL prime factorial ORIGINAL running factorial product57，不以小數近似替代。
• S183 · 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。
• S182 · premise_and_result_audit — 以精確有理數重算 Wilson ORIGINAL prime factorial ORIGINAL running factorial product56，不以小數近似替代。
• S181 · 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。
• S180 · premise_and_result_audit — 以精確有理數重算 Wilson ORIGINAL prime factorial ORIGINAL running factorial product55，不以小數近似替代。
• S179 · 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。
• S178 · premise_and_result_audit — 以精確有理數重算 Wilson ORIGINAL prime factorial ORIGINAL running factorial product54，不以小數近似替代。
• S177 · 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。
• S176 · premise_and_result_audit — 以精確有理數重算 Wilson ORIGINAL prime factorial ORIGINAL running factorial product53，不以小數近似替代。
• S175 · 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。
• S174 · premise_and_result_audit — 以精確有理數重算 Wilson ORIGINAL prime factorial ORIGINAL running factorial product52，不以小數近似替代。
• S173 · 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。
• S172 · premise_and_result_audit — 以精確有理數重算 Wilson ORIGINAL prime factorial ORIGINAL running factorial product51，不以小數近似替代。
• S171 · 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。
• S170 · premise_and_result_audit — 以精確有理數重算 Wilson ORIGINAL prime factorial ORIGINAL running factorial product50，不以小數近似替代。
• S169 · 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。
• S168 · premise_and_result_audit — 以精確有理數重算 Wilson ORIGINAL prime factorial ORIGINAL running factorial product49，不以小數近似替代。
• S167 · 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。
• S166 · premise_and_result_audit — 以精確有理數重算 Wilson ORIGINAL prime factorial ORIGINAL running factorial product48，不以小數近似替代。
• S165 · 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。
• S164 · premise_and_result_audit — 以精確有理數重算 Wilson ORIGINAL prime factorial ORIGINAL running factorial product47，不以小數近似替代。
• S163 · 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。
• S162 · premise_and_result_audit — 以精確有理數重算 Wilson ORIGINAL prime factorial ORIGINAL running factorial product46，不以小數近似替代。
• S161 · 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。
• S160 · premise_and_result_audit — 以精確有理數重算 Wilson ORIGINAL prime factorial ORIGINAL running factorial product45，不以小數近似替代。
• S159 · 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。
• S158 · premise_and_result_audit — 以精確有理數重算 Wilson ORIGINAL prime factorial ORIGINAL running factorial product44，不以小數近似替代。
• 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 ORIGINAL prime factorial ORIGINAL running factorial product43，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 ORIGINAL prime factorial ORIGINAL running factorial product42，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 ORIGINAL prime factorial ORIGINAL running factorial product41，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 ORIGINAL prime factorial ORIGINAL running factorial product40，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 ORIGINAL prime factorial ORIGINAL running factorial product39，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 ORIGINAL prime factorial ORIGINAL running factorial product38，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 ORIGINAL prime factorial ORIGINAL running factorial product37，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 ORIGINAL prime factorial ORIGINAL running factorial product36，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 ORIGINAL prime factorial ORIGINAL running factorial product35，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 ORIGINAL prime factorial ORIGINAL running factorial product34，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 ORIGINAL prime factorial ORIGINAL running factorial product33，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 ORIGINAL prime factorial ORIGINAL running factorial product32，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 ORIGINAL prime factorial ORIGINAL running factorial product31，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 ORIGINAL prime factorial ORIGINAL running factorial product30，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 ORIGINAL prime factorial ORIGINAL running factorial product29，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 ORIGINAL prime factorial ORIGINAL running factorial product28，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 ORIGINAL prime factorial ORIGINAL running factorial product27，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 ORIGINAL prime factorial ORIGINAL running factorial product26，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 ORIGINAL prime factorial ORIGINAL running factorial product25，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 ORIGINAL prime factorial ORIGINAL running factorial product24，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 ORIGINAL prime factorial ORIGINAL running factorial product23，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 ORIGINAL prime factorial ORIGINAL running factorial product22，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 ORIGINAL prime factorial ORIGINAL running factorial product21，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 ORIGINAL prime factorial ORIGINAL running factorial product20，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 ORIGINAL prime factorial ORIGINAL running factorial product19，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 ORIGINAL prime factorial ORIGINAL running factorial product18，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 ORIGINAL prime factorial ORIGINAL running factorial product17，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 ORIGINAL prime factorial ORIGINAL running factorial product16，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 ORIGINAL prime factorial ORIGINAL running factorial product15，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 ORIGINAL prime factorial ORIGINAL running factorial product14，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 ORIGINAL prime factorial ORIGINAL running factorial product13，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 ORIGINAL prime factorial ORIGINAL running factorial product12，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 ORIGINAL prime factorial ORIGINAL running factorial product11，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 ORIGINAL prime factorial ORIGINAL running factorial product10，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 ORIGINAL prime factorial ORIGINAL running factorial product9，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 ORIGINAL prime factorial ORIGINAL running factorial product8，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 ORIGINAL prime factorial ORIGINAL running factorial product7，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 ORIGINAL prime factorial ORIGINAL running factorial product6，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 ORIGINAL prime factorial ORIGINAL running factorial product5，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 ORIGINAL prime factorial ORIGINAL running factorial product4，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 ORIGINAL prime factorial ORIGINAL running factorial product3，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 ORIGINAL prime factorial ORIGINAL running factorial product2，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 ORIGINAL prime factorial ORIGINAL running factorial product1，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 — 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。
• 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 — 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。
• 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 — 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。
• 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 — 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。
• 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 — 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。
• 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 — 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。
• 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 — 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。
• 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 — 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。
• 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 — 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。
• 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 — 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。
• 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 — 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。
• 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 — 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。
• 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 — 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。
• 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 — 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。
• 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 — 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。
• 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 — 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。
• 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 — 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。
• 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 — 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。
• 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 — 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。
• 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 — 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。
• 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 — 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。
• 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 — 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。
• 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 — 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。
• 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 — 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。
• 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 — 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。
• 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 — 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。
• 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 — 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。
• 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 — 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。
• 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 — 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。
• 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 — 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。
• 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 — 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。
• 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 — 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。
• 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 — 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。
• 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 — 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。
• 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 — 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。
• 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

(71, [[1, 1], [2, 36], [3, 24], [4, 18], [5, 57], [6, 12], [7, 61], [8, 9], [9, 8], [10, 64], [11, 13], [12, 6], [13, 11], [14, 66], [15, 19], [16, 40], [17, 46], [18, 4], [19, 15], [20, 32], [21, 44], [22, 42], [23, 34], [24, 3], [25, 54], [26, 41], [27, 50], [28, 33], [29, 49], [30, 45], [31, 55], [32, 20], [33, 28], [34, 23], [35, 69], [36, 2], [37, 48], [38, 43], [39, 51], [40, 16], [41, 26], [42, 22], [43, 38], [44, 21], [45, 30], [46, 17], [47, 68], [48, 37], [49, 29], [50, 27], [51, 39], [52, 56], [53, 67], [54, 25], [55, 31], [56, 52], [57, 5], [58, 60], [59, 65], [60, 58], [61, 7], [62, 63], [63, 62], [64, 10], [65, 59], [66, 14], [67, 53], [68, 47], [69, 35], [70, 70]], [1, 70], [[2, 36, 1], [3, 24, 1], [4, 18, 1], [5, 57, 1], [6, 12, 1], [7, 61, 1], [8, 9, 1], [10, 64, 1], [11, 13, 1], [14, 66, 1], [15, 19, 1], [16, 40, 1], [17, 46, 1], [20, 32, 1], [21, 44, 1], [22, 42, 1], [23, 34, 1], [25, 54, 1], [26, 41, 1], [27, 50, 1], [28, 33, 1], [29, 49, 1], [30, 45, 1], [31, 55, 1], [35, 69, 1], [37, 48, 1], [38, 43, 1], [39, 51, 1], [47, 68, 1], [52, 56, 1], [53, 67, 1], [58, 60, 1], [59, 65, 1], [62, 63, 1]], self_inverse_residues_1_and_p_minus_1, 70, 是)

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。