I have posted Problem 7 for reference below. Please only attempt the problem above. Thank you!

(a) Use Problem 7 to show that (p - 1)! -1 (mod p) for every -1)-1 . 2 . . . . . (p-1) to pair up each (b) Show by example that Wilson't theorem may fail if n is not a prime number p. (This congruence is called Wilson's theorem.) Hint: In the product p element x with its multiplicative inverse a-1 in Z prime