Recall the definition of n! (read n factorial"):

n! = (n)(n-1)(n-2) ….(2)(1) =∏(k)

In both (a) and (b) below, suppose p≥3 is prime.

(a) Prove that if x∈ Zpx is a solution to x square ≡1 (mod p), then x ≡±1 (mod p).

(b) Prove that (p-1)!≡±1 (mod p)

Zpx x shoud be above p