Question 89
Find all functions $f : \mathbb{R} \to \mathbb{R}$ that satisfy $f(0) = 0$, $f(1) = 2013$ and
$$
(x - y) (f(f(x)^2) - f(f(y)^2)) = (f(x) - f(y)) (f(x)^2 - f(y)^2)
$$
for all real numbers $x, y$.
$$
(x - y) (f(f(x)^2) - f(f(y)^2)) = (f(x) - f(y)) (f(x)^2 - f(y)^2)
$$
for all real numbers $x, y$.