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diophantine (ab)^{2015} = (a^2 + b^2)^m

Source: New Zealand NZMOC Camp Selection Problems 2015 p4

September 19, 2021
number theoryDiophantine equationdiophantine

Problem Statement

For which positive integers mm does the equation: (ab)2015=(a2+b2)m(ab)^{2015} = (a^2 + b^2)^m have positive integer solutions?
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