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a^2 +b^2 +x^2 = y^2 has an integer solution x,y iff product ab is even

Source: 1993 Swedish Mathematical Competition p3

April 2, 2021
Evennumber theorydiophantineDiophantine equation

Problem Statement

Assume that aa and bb are integers. Prove that the equation a2+b2+x2=y2a^2 +b^2 +x^2 = y^2 has an integer solution x,yx,y if and only if the product abab is even.
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