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2023 OIM Problems/Problem 2

Revision as of 03:13, 14 December 2023 by Tomasdiaz (talk | contribs) (Created page with "== Problem == Let <math>\mathbb{Z}</math> be the set of integers. Find all functions <math>f: \mathbb{Z} \to \mathbb{Z}</math> such that: <cmath>2023f(f(x))+2022x^2=2022f(x)+...")
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Problem

Let $\mathbb{Z}$ be the set of integers. Find all functions $f: \mathbb{Z} \to \mathbb{Z}$ such that:

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

for each integer $x$.

Solution

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See also

https://sites.google.com/associacaodaobm.org/oim-brasil-2023/pruebas

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