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1

Part of 2023 Turkey MO (2nd round)

Problems(1)

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

Source: 2023 Turkey NMO 2nd Round P1

12/21/2023
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.
number theoryconstruction