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diophantine (x^2 + y^2)^n = (xy)^{2016} with no solutions

Source: New Zealand NZMOC Camp Selection Problems 2016 p7

September 19, 2021
diophantineDiophantine equationnumber theory

Problem Statement

Find all positive integers nn for which the equation (x2+y2)n=(xy)2016(x^2 + y^2)^n = (xy)^{2016} has positive integer solutions.
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