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f(x^k*y^k) = x*y*f(x)*f(y)

Source: Austrian Federal Competition 2013, part 2, problem 2

June 18, 2013

functionalgebra proposedalgebra

Problem Statement

Let

k

be an integer. Determine all functions

f\colon \mathbb{R}\to\mathbb{R}

with

f(0)=0

and f(x^ky^k)=xyf(x)f(y)\qquad \mbox{for } x,y\neq 0.