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a^2 + 4b and b^2 + 4a perfect squares

Source: Germany Federal - Bundeswettbewerb Mathematik 2012, round 1, p2

April 11, 2020
number theoryPerfect SquaresPerfect Square

Problem Statement

Are there positive integers aa and bb such that both a2+4ba^2 + 4b and b2+4ab^2 + 4a are perfect squares?
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