International Mathematical Olympiad 2006 Problem 3

Determine the least real number $M$ such that the inequality $$\left| ab(a^2 - b^2) + bc(b^2 - c^2) + ca(c^2 - a^2) \right| \leq M(a^2 + b^2 + c^2)^2$$ holds for all real numbers $a$, $b$ and $c$.