Let p be an odd prime. (a) Prove that x2 = 1 (mod p) if and only if x = £1 (mod p). (b) Let [a] E Zp with [a] # [0]. Use (a) to prove that if [a] -1 = [a], then [a] = [1] or [a] = [p – 1] + [1]. (c) Use (b) to prove Wilson's Theorem which states that (p - 1)! = -1 (mod p). Remark: One can verify easily that Wilson's Theorem also holds if p = 2.