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xyd = x + y + d^2 where d = gcd(x, y)

Source: 2023 Austrian Regional Competition For Advanced Students p4

March 26, 2024
number theoryGCDgreatest common divisorDiophantine equation

Problem Statement

Determine all pairs (x,y)(x, y) of positive integers such that for d=gcd(x,y)d = gcd(x, y) the equation xyd=x+y+d2xyd = x + y + d^2 holds.
(Walther Janous)
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