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A Factorial That's Always One Less Than a Multiple of the Next Prime
Take any prime number pp p. Multiply together every integer from 11 1 to p−1p-1 p−1. The result is always exactly one less than a multiple of pp p. Always. This is Wilson's Theorem — and the proof uses nothing more than a clever pairing argument that anyone can follow. One of the most beautiful results in all of number theory. Try it ...
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