A problem about polynomial

Question

Let $P(x)$ is an integer polynomial, deg$=n$, irreducible on $Z[x]$. $a_1$,$a_2$,$a_3$,$...$,an are roots of $P(x)$. Prove that if $p$ is a prime number then $p|(a_1+a_2+...+a_n)-(a_1^p+a_2^p+....+a_n^p)$ . (Sorry for my bad English)