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Funky number theory

Source: Kyiv City MO 2024 Round 1, Problem 11.5

January 28, 2024
functional equationnumber theoryFunctional Equations

Problem Statement

Find all functions f:Nā†’Nf : \mathbb{N} \to \mathbb{N} such that for any positive integers m,nm, n the number (f(m))2+2mf(n)+f(n2)(f(m))^2+ 2mf(n) + f(n^2) is the square of an integer.
Proposed by Fedir Yudin
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