OIM 2023 Problem 2

Seja $\mathbb{Z}$ o conjunto dos inteiros. Encontre todas as funções $f: \mathbb{Z} \rightarrow \mathbb{Z}$ tais que:

$2023f(f(x)) + 2022x^2 = 2022f(x) + 2023[f(x)]^2 + 1$

para todo inteiro $x$ .

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Solutions

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