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If n|p-1 and p|n^3-1, then 4p-3 is a square

Source: Czech-Polish-Slovak 2002 Q4

April 28, 2013
number theory unsolvednumber theory

Problem Statement

An integer n>1n > 1 and a prime pp are such that nn divides p−1p-1, and pp divides n3−1n^3 - 1. Prove that 4p−34p - 3 is a perfect square.
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