First 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.
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.