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(x^2 + y^2)/(x + y)= 10 diophantine

Source: 2019 Austrian Mathematical Olympiad Junior Regional Competition , Problem 1

December 18, 2020
number theoryDiophantine equationdiophantine

Problem Statement

Let xx and yy be integers with x+y≠0x + y \ne 0. Find all pairs (x,y)(x, y) such that x2+y2x+y=10.\frac{x^2 + y^2}{x + y}= 10.
(Walther Janous)
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