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Find all functions (x+y)f(f(x)y)=x^2f(f(x)+f(y)) - Iran NMO 2005 - Problem6

Source: Iran NMO 2005 - Problem 6

September 21, 2010
functionalgebra proposedalgebrafunctional equation

Problem Statement

Find all functions f:R+ā†’R+f:\mathbb{R}^{+}\to \mathbb{R}^{+} such that for all positive real numbers xx and yy, the following equation holds: (x+y)f(f(x)y)=x2f(f(x)+f(y)).(x+y)f(f(x)y)=x^2f(f(x)+f(y)).
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