Question 59
Find all functions $f: \mathbb{N} \rightarrow \mathbb{N}$ (where $\mathbb{N}$ is the set of the natural numbers and is assumed to contain $0$), such that
$$
f\left(x^{2}\right)-f\left(y^{2}\right)=f(x+y) f(x-y)
$$
for all $x, y \in \mathbb{N}$ with $x \geq y$.
$$
f\left(x^{2}\right)-f\left(y^{2}\right)=f(x+y) f(x-y)
$$
for all $x, y \in \mathbb{N}$ with $x \geq y$.