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prime p and perfect square

Source: Turkey NMO 2008 Problem 2

December 2, 2008
quadraticsnumber theory

Problem Statement

a \minus{} ) Find all prime p p such that \dfrac{7^{p \minus{} 1} \minus{} 1}{p} is a perfect square b \minus{} ) Find all prime p p such that \dfrac{11^{p \minus{} 1} \minus{} 1}{p} is a perfect square