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n|(p-1) and p | (n^3-1) => (4p-3) square

Source: 2010 Dutch IMO TST1 P3

January 10, 2020
number theoryPerfect Square

Problem Statement

Let n\ge  2 be a positive integer and pp a prime such that n∣p−1n|p-1 and p∣n3−1p | n^3-1. Show 4p−3 4p-3 is a square.
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