Question 17
Let $n$ be a positive integer. Find all functions $f : \mathbb{R} \to \mathbb{R}$ that satisfy the equation
$$ f(x)^n f(x+y) = f(x)^{n+1} + x^n f(y) $$
for all $x, y \in \mathbb{R}$.
$$ f(x)^n f(x+y) = f(x)^{n+1} + x^n f(y) $$
for all $x, y \in \mathbb{R}$.