Question 91
Let $\mathbb{R}$ denote the set of all real numbers. Determine all injective functions $f: \mathbb{R} \to \mathbb{R}$ such that
$$
(f(a) - f(b))(f(b) - f(c))(f(c) - f(a)) = f(ab^2 + bc^2 + ca^2) - f(a^2b + b^2c + c^2a)
$$
for all real numbers $a, b, c$.
$$
(f(a) - f(b))(f(b) - f(c))(f(c) - f(a)) = f(ab^2 + bc^2 + ca^2) - f(a^2b + b^2c + c^2a)
$$
for all real numbers $a, b, c$.