Question 5
Find all functions $f:\mathbb R\to\mathbb R$ such that $f(0)=0$, $f(1)=2013$, and, for all real $x,y$,
$$(x-y)\bigl(f(f^2(x))-f(f^2(y))\bigr)$$
$$=(f(x)-f(y))\bigl(f^2(x)-f^2(y)\bigr),$$
where $f^2(x)=(f(x))^2$.
$$(x-y)\bigl(f(f^2(x))-f(f^2(y))\bigr)$$
$$=(f(x)-f(y))\bigl(f^2(x)-f^2(y)\bigr),$$
where $f^2(x)=(f(x))^2$.