Using Exercise 27, deduce the half of Wilson's theorem that states that if p is a prime, then (p - 1)! = -1 (mod p). [The other half states that if n is an integer > 1 such that (n - 1)! = -1 (mod n), then n is a prime. Just think what the remainder of (n - 1)! would be modulo n if n is not a prime.]
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