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3n + 1 and 10n + 1 are perfect squares , then 29n+11 not prime

Source: Germany Federal - Bundeswettbewerb Mathematik 2011, round 2, p2

April 15, 2020
number theoryprimeCompositecomposite numberPerfect SquaresPerfect Square

Problem Statement

Proove that if for a positive integer nn , both 3n+13n + 1 and 10n+110n + 1 are perfect squares , then 29n+1129n + 11 is not a prime number.
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