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f[x^k + f(y)] = y +[f(x)]^k

Source: China TST 2001, problem 3

May 22, 2005
functionalgebrapolynomialfunctional equationalgebra unsolved

Problem Statement

For a given natural number k>1k > 1, find all functions f:R→Rf:\mathbb{R} \to \mathbb{R} such that for all x,y∈Rx, y \in \mathbb{R}, f[xk+f(y)]=y+[f(x)]kf[x^k + f(y)] = y +[f(x)]^k.
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