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diophantine x^{2018}-y^{2018}=(xy)^{2017} for non-negative integers

Source: Finland 2018, p5

September 8, 2019
number theoryDiophantine equationdiophantine

Problem Statement

Solve the diophantine equation x2018āˆ’y2018=(xy)2017x^{2018}-y^{2018}=(xy)^{2017} when xx and yy are non-negative integers.