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p^2+2q^2+334=[p^2,q^2] , where p,q coprime

Source: Greece JBMO TST 2012 p2

April 29, 2019
number theoryleast common multiplecoprimeDiophantine equation

Problem Statement

Find all pairs of coprime positive integers (p,q)(p,q) such that p2+2q2+334=[p2,q2]p^2+2q^2+334=[p^2,q^2] where [p2,q2][p^2,q^2] is the leact common multiple of p2,q2p^2,q^2 .
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