Wilson’s Theorem

Wilson’s theorem states that for any prime integer p, (p-1)! \equiv -1 \pmod{p}. I wrote this on the board at the beginning of lecture as a warm-up for my students. But when asked to give a proof, I became dissatisfied with my reasoning when a student said he didn’t understand the argument, and I could not manage to explain it. I believe this is a correct proof.

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