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(n+1)2^n, (n+3)2^{n+2} not perfect squares for the same n

Source: Greece JBMO TST 2015 p3

April 29, 2019
number theoryPerfect SquaresPerfect Squarepositive integer

Problem Statement

Prove that there is not a positive integer nn such that numbers (n+1)2n,(n+3)2n+2(n+1)2^n, (n+3)2^{n+2} are both perfect squares.
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