MathNet 2020 — Math Olympiad Vault — Part 05 Question 128

Let $n$ be a positive integer. Show that there are functions $f : \mathbb{R} \to \mathbb{R}$ satisfying $f(f(x) + y f(y)) = x + (f(y))^n$, for any $x, y \in \mathbb{R}$, if and only if $n = 2$. Determine those functions.

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