Problem

Source: China TST 2001, problem 3

Tags: function, algebra, polynomial, functional equation, algebra unsolved



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