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Diophantine equation

Source: Greek National mathematical olympiad,Problem 1

February 29, 2016
number theoryDiophantine equation

Problem Statement

Find all triplets of nonnegative integers (x,y,z)(x,y,z) and x≤yx\leq y such that x2+y2=3⋅2016z+77x^2+y^2=3 \cdot 2016^z+77
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