Question 22
Let $\mathbb{Z}$ denote the set of all integers. Find all functions $f: \mathbb{Z} \to \mathbb{Z}$ such that $f(0) = 0$ and for all integers $x, y$,
$$
f(x + f(y))f(y + f(x)) = (2x + f(y - x))(2y + f(x - y)) \text{ holds.}
$$
$$
f(x + f(y))f(y + f(x)) = (2x + f(y - x))(2y + f(x - y)) \text{ holds.}
$$