KMO 2020 Problem 1

Determine all functions $f:\mathbb{R}\rightarrow\mathbb{R}$ such that $x^2f(x)+yf(y^2)=f(x+y)f(x^2-xy+y^2)$ for all $x,y\in\mathbb{R}$ .

Dataset text AI-MO AoPS. Quoted with source.

Solutions

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