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MathNet 2021 — Part 03 Question 24

Math Olympiad Vault · MathNet 2021 — Part 03

Question 24

Find all functions $f : \mathbb{R} \to \mathbb{R}$ such that for any $x, y \in \mathbb{R}$,
$$ f(xf(y) + y^{2021}) = yf(x) + (f(y))^{2021}. $$
(Contributed by Fu Yunhao)