number theory - Show that it is impossible that $P(a)=b$, $P(b)=c$, and $P(c)=a$ at the same time.

Let $a, b, c$ be distinct integers, and let $P$ be a polynomial with integer coefficients. Show that it is impossible that $P(a)=b$, $P(b)=c$, and $P(c)=a$ at the same time.