Question 111
Let $n \in \mathbb{N}^*$. Determine all functions $f : \mathbb{R} \to \mathbb{R}$ that satisfy:
$$
f(x + y^{2n}) = f(f(x)) + y^{2n-1}f(y),
$$
for all $x, y \in \mathbb{R}$, and for which the equation $f(x) = 0$ has a unique solution.
$$
f(x + y^{2n}) = f(f(x)) + y^{2n-1}f(y),
$$
for all $x, y \in \mathbb{R}$, and for which the equation $f(x) = 0$ has a unique solution.