1. (a) Let p be a prime. Prove that in (Z/pZ)[x], xp−x= x(x−1)(x−2)···(x−(p−1)). (b) Use your...

1. (a) Let p be a prime. Prove that in (Z/_pZ)[x], x^p−x= x(x−1)(x−2)···(x−(p−1)).

(b) Use your answer to part (a) to prove that for any prime p, (p−1)!≡−1 (modp).

Expert Solution

Colby Messinger answered 4 months ago

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