3 Wilson's Theorem Wilson's Theorem states the following is true if and only if p is prime: (p l)! E 1 (mod p). Prove both directions (it holds if AND only if p is prime). Hint for the if direction: Consider rearranging the terms in ( p l)! = 1 - 2 ----- (p l) to pair up terms with their inverses, when possible. What terms are left unpaired? Hint for the only if direction: If p is composite, then it has some prime factor q. What can we say about (p 1)! (mod q)