Question 61
Let $a_{1}, a_{2}, a_{3}, a_{4}$ be four distinct integers and let $P(x)$ be a polynomial with integer coefficients such that
$$
P\left(a_{1}\right)=P\left(a_{2}\right)=P\left(a_{3}\right)=P\left(a_{4}\right)=1 .
$$
a. Prove that there is no integer $n$ such that $P(n)=12$.
b. Is there a polynomial $P(x)$ that satisfies the condition $(*)$ and an integer $n$ such that $P(n)=1998$ ?
$$
P\left(a_{1}\right)=P\left(a_{2}\right)=P\left(a_{3}\right)=P\left(a_{4}\right)=1 .
$$
a. Prove that there is no integer $n$ such that $P(n)=12$.
b. Is there a polynomial $P(x)$ that satisfies the condition $(*)$ and an integer $n$ such that $P(n)=1998$ ?