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(m - 1)! + 1 = m^n , m>5 diophantine

Source: Singapore Senior Math Olympiad 2000 2nd Round p2 SMO

April 4, 2020

factorialDiophantine equationdiophantinenumber theory

Problem Statement

Prove that there exist no positive integers

m

and

n

such that

m > 5

and

(m - 1)! + 1 = m^n