Question: that 7! 9! 1 (mod 71) because 9 8 = 72 1 (mod 71) (from which we conclude that 9! 7! (mod 71)) and (again

that 7! 9! 1 (mod 71) because 9 8 = 72 1 (mod 71) (from which we conclude that 9! 7! (mod 71)) and (again using 9 8 1 (mod 71)) 7! = 7 6 5 4 3 2 = (2 4) (3 6) 7 5 = (8 9) 2 7 5 1 70 1 (mod 71) . By Wilson's Theorem, since 71 is prime, 70! 1 (mod 71). Moreover, p r r (mod p ), so it implies that 1 70! 70 69 68 67 66 65 64 63! ( 1) 7 7!63! 63! (mod 71) and 1 70! 70 69 68 67 66 65 64 63 62 61! ( 1) 9 9!61! 61! (mod 71)

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