Prove that for any positive number $a,b,c$ and any nonnegative integer $p$ $$a^{p+2}+b^{p+2}+c^{p+2}\ge a^pbc+b^pca+c^pab.$$
Source: Croatia MO 2002 1st Grade P2
Tags: Inequality, inequalities
Prove that for any positive number $a,b,c$ and any nonnegative integer $p$ $$a^{p+2}+b^{p+2}+c^{p+2}\ge a^pbc+b^pca+c^pab.$$