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xf(x + xy) = xf(x) + f(x^2)f(y)

Source: MEMO 2008, Team, Problem 5

September 10, 2008
functionalgebra unsolvedalgebra

Problem Statement

Determine all functions f:R↦R f: \mathbb{R} \mapsto \mathbb{R} such that x f(x \plus{} xy) \equal{} x f(x) \plus{} f \left( x^2 \right) f(y)   \forall x,y \in \mathbb{R}.
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