Question 133
Find all surjective functions $f: Z \to Z$ such that for all integers $x, y, z$
$$
f(xyz + xf(y) + yf(z) + zf(x)) = f(x)f(y)f(z) \text{ holds.}
$$
Note: here $Z$ denotes the set of all integers.
$$
f(xyz + xf(y) + yf(z) + zf(x)) = f(x)f(y)f(z) \text{ holds.}
$$
Note: here $Z$ denotes the set of all integers.