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2011 Japan Mathematical Olympiad Finals Problem 4

Source: Japanese MO Finals 2011, India Postal 2016 Set 1, P2

February 11, 2011
functionquadraticsalgebra proposedalgebra

Problem Statement

Find all functions f:R→R f : \mathbb{R} \to\mathbb{R} such that f(f(x)−f(y))=f(f(x))−2x2f(y)+f(y2)f(f(x)-f(y))=f(f(x))-2x^2f(y)+f(y^2) for all x,y∈R.x,y \in \mathbb{R}.
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