Question: Using Exercise 28 below, find the remainder of 34! modulo 37. Data from Exercise 28 Using Exercise 27, deduce the half of Wilson's theorem that

Using Exercise 28 below, find the remainder of 34! modulo 37.

Data from Exercise 28

Using Exercise 27, deduce the half of Wilson's theorem that states that if pis 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 - l)! would be modulo n if n is not a prime.]

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