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Find three functions

Source: China TST 1990, problem 6

June 27, 2005
functionalgebra unsolvedalgebra

Problem Statement

Find all functions f,g,h:RRf,g,h: \mathbb{R} \mapsto \mathbb{R} such that f(x)g(y)=(xy)h(x+y)f(x) - g(y) = (x-y) \cdot h(x+y) for x,yR.x,y \in \mathbb{R}.