Question 35
Find all nonzero polynomials $P(x)$ with integer coefficients that satisfy the following property: whenever $a$ and $b$ are relatively prime integers, then $P(a)$ and $P(b)$ are relatively prime as well. Prove that your answer is correct. (Two integers are relatively prime if they have no common prime factors. For example, $-70$ and $99$ are relatively prime, while $-70$ and $15$ are not relatively prime.)