IT-CESENATICO 1998 Problem 5

Suppose $a_1,a_2,a_3,a_4$ are distinct integers and $P(x)$ is a polynomial with integer coefficients satisfying $P(a_1) = P(a_2) = P(a_3) = P(a_4) = 1$ . (a) Prove that there is no integer $n$ such that $P(n) = 12$ . (b) Do there exist such a polynomial and $a_n$ integer $n$ such that $P(n) = 1998$ ?