Question 109
Let $n$ be a positive integer. Determine all functions $f : \mathbb{R} \to \mathbb{R}$ such that
$$
(f(x))^n f(x + y) = (f(x))^{n+1} + x^n f(y)
$$
holds for all real numbers $x, y$.
$$
(f(x))^n f(x + y) = (f(x))^{n+1} + x^n f(y)
$$
holds for all real numbers $x, y$.