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2016 JBMO TST- Macedonia, problem 5

Source: 2016 JBMO TST- Macedonia

May 27, 2019
JuniorJMMO2016number theoryMacedoniagreatest common divisor

Problem Statement

Solve the following equation in the set of positive integers x+y2+(GCD(x,y))2=xyā‹…GCD(x,y)x + y^2 + (GCD(x, y))^2 = xy \cdot GCD(x, y).
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