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\frac{n^2+m^2}{m^4+n}=k

Source: 2023 Turkey NMO 2nd Round P1

December 21, 2023
number theoryconstruction

Problem Statement

Prove that there exist infinitely many positive integers kk such that the equation n2+m2m4+n=k\frac{n^2+m^2}{m^4+n}=k don't have any positive integer solution.
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