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Prove that 4p-3 is a square - Iran NMO 2005 - Problem1

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September 21, 2010
number theoryLte

Problem Statement

Let n,p>1n,p>1 be positive integers and pp be prime. We know that n∣p−1n|p-1 and p∣n3−1p|n^3-1. Prove that 4p−34p-3 is a perfect square.
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