p is prime, not 2. Thanks in advance
There is no p in your expression!
he had to have meant (mod p)
p = n
This is not a difficult problem, but you must understand Wilson's Theorem. Wilson, by the way, was never a mathematician, and as a student went on to become a lawyer.
He is credited with noticing the theorem, but was unable to prove it. So much for the immortal glory of a name theorem!
So what is your question and what have you tried to solve it?
I thought it was clear what the question was(since the others understood): prove that this is true for every n prime, n!= 2. Using the Wilson theorem, I didn't go far:
((n-1)/2)!*((n+1)/2)*((n+3)/2)*...*(n-1) = -1 (mod n).
Nevermind guys, I figured it out. Thanks for your input.
Separate names with a comma.