Problem

Wilson’s theorem says that a number N is prime if and only if(a) If p is prime, then we kn...

Wilson’s theorem says that a number N is prime if and only if

(a) If p is prime, then we know every number 1 ≤ x

(b) By pairing up multiplicative inverses, show that (p − 1)! ≡ −1 (mod p) for prime p.

(c) Show that if N is not prime, then (N − 1)! (mod N). (Hint: Consider d = gcd(N, (N − 1)!).)

(d) Unlike Fermat’s Little theorem, Wilson’s theorem is an if-and-only-if condition for primality. Why can’t we immediately base a primality test on this rule?

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Wilson’s theorem says that a number N is prime if and only if(a) If p is prime, then we kn...

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