INMO 1992 Problem 6

Let $f(x)$ be a polynomial in $x$ with integer coefficients and suppose that for five distinct integers $a_1, \ldots, a_5$ one has $f(a_1) = f(a_2) = \ldots = f(a_5) = 2$ . Show that there does not exist an integer $b$ such that $f(b) = 9$ .