Question 96
Let $\mathbb{Z}$ be the set of all integers. Determine all functions $f : \mathbb{Z} \to \mathbb{Z}$ such that
$$
f(f(x) + f(y)) + f(x)f(y) = f(x + y)f(x - y)
$$
holds for all $x, y \in \mathbb{Z}$.
$$
f(f(x) + f(y)) + f(x)f(y) = f(x + y)f(x - y)
$$
holds for all $x, y \in \mathbb{Z}$.