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x,y coprime, x + 3y^2 perfect square, x^2 + 9y^4 not a perfect square

Source: KJMO 2011 p3

May 4, 2019
number theorycoprimePerfect Square

Problem Statement

Let x,yx, y be positive integers such that gcd(x,y)=1gcd(x, y) = 1 and x+3y2x + 3y^2 is a perfect square. Prove that x2+9y4x^2 + 9y^4 can't be a perfect square.
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