Question 84
Find all triples $(a; b; c)$ of real numbers for which there exists a non-zero function $f$, $f: \mathbb{R} \to \mathbb{R}$, such that
$$
af(xy + f(z)) + bf(yz + f(x)) + cf(zx + f(y)) = 0
$$
for all real $x, y, z$.
$$
af(xy + f(z)) + bf(yz + f(x)) + cf(zx + f(y)) = 0
$$
for all real $x, y, z$.