So I've been working on this problem for too long now and I need some advice as to how to proceed. I've tried using induction and I've also tried plugging in concrete values to try and discern a pattern to no avail. I DO know that Wilson's Theorem applies.

Wilson's Theorem

If p is a prime, then (p-1)! $\displaystyle \equiv$ -1 (mod p)

Show that if p is an odd prime and a and b are non negative integers with a+b=p-1, then a!b! + (-1)^a $\displaystyle \equiv$ 0 (mod p)Problem