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JBMO 2022 Problem 3

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Find all quadruples of positive integers (p,q,a,b)(p, q, a, b), where pp and qq are prime numbers and a>1a>1, such that

pa=1+5qbp^{a}=1+5 q^{b}

Dataset text NuminaMath olympiads. Quoted with source.

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(4,4,3,2) \text{ and } (4,1,2,3)

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