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pn|(p-1)^n+1

Source: Turkey Team Selection Test 2019 Day 3 Problem 8

March 26, 2019
number theory

Problem Statement

Let p>2p>2 be a prime number, m>1m>1 and nn be positive integers such that mpn−1mn−1\frac {m^{pn}-1}{m^n-1} is a prime number. Show that: pn∣(p−1)n+1pn\mid (p-1)^n+1
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