MathDB

Find all nonzero polynomials

P(x)

with integers 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.)

Problem Statement