CZ-SK-MO 1986 Problem 2

Let $P(x)$ be a polynomial with integer coefficients of degree $n \ge 3$ . If $x_1,...,x_m$ ( $n\ge m\ge3$ ) are different integers such that $P(x_1) = P(x_2) = ... = P(x_m) = 1$ , prove that $P$ cannot have integer roots$.