The quantity (p − 1)! (mod p) appeared in our proof of Fermat’s Little Theorem, although we didn’t need to know its value.
(a) Compute (p − 1)! (mod p) for some small values of p, find a pattern, and make a conjecture.
(b) Prove that your conjecture is correct. [Try to discover why (p − 1)! (mod p) has the value it does for small values of p, and then generalize your observation to prove the formula for all values of p.]
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