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2018 PAMO Shortlist: Diophantine equation $(x^2 + y^2)^n = (xy)^{2018}$

Source: 2018 Pan-African Shortlist - N7

May 6, 2019
number theoryDiophantine equation

Problem Statement

Find all non-negative integers nn for which the equation (x2+y2)n=(xy)2018 {\left( x^2 + y^2 \right)}^n = {(xy)}^{2018} admits positive integral solutions.
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