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Korea Second Round 2011

Source: Korea Second Round 2011 #2

August 21, 2011
modular arithmeticnumber theorygreatest common divisornumber theory unsolved

Problem Statement

Let x,yx, y be positive integers such that gcd⁡(x,y)=1\gcd(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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