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Second hint to puzzle 137: Factorial plus one equals prime power?

Suppose (p − 1)! + 1 = pn, for some positive integer n.  Subtract 1 from both sides of the equation, and divide by p − 1, yielding

(p − 2)! = pn−1 + pn−2 + ... + p + 1.

Show that if m is a composite integer greater than 4, then (m − 1)! is divisible by m.