Question 21
Find all functions $f : \mathbb{R} \to \mathbb{R}$ such that
$$
f(f(x+y)f(x-y)) = x^2 - y f(y)
$$
for all $x, y \in \mathbb{R}$.
$$
f(f(x+y)f(x-y)) = x^2 - y f(y)
$$
for all $x, y \in \mathbb{R}$.
MathNet 2012 Question 21
Math Olympiad Vault · MathNet 2012