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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)! -1 (mod p)
Problem
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 0 (mod p)