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2022 Junior Balkan MO, Problem 3

Source: 2022 JBMO Problem 3

June 30, 2022
number theoryprime numbersDiophantine equationJBMO

Problem Statement

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+5qb.p^a = 1 + 5q^b.
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