Determine the least real number
![M](/media/m/f/7/f/f7f312cf6ba459a332de8db3b8f906c4.png)
such that the inequality
holds for all real numbers
![a](/media/m/6/d/2/6d2832265560bb67cf117009608524f6.png)
,
![b](/media/m/e/e/c/eec0d7323095a1f2101fc1a74d069df6.png)
and
![c](/media/m/e/a/3/ea344283b6fa26e4a02989dd1fb52a51.png)
.
%V0
Determine the least real number $M$ such that the inequality
$\left|ab\left(a^{2}-b^{2}\right)+bc\left(b^{2}-c^{2}\right)+ca\left(c^{2}-a^{2}\right)\right| \leq M\left(a^{2}+b^{2}+c^{2}\right)^2$
holds for all real numbers $a$, $b$ and $c$.