MathDB

Let

f(x)

and

g(x)

be polynomials with integer coefficients. Prove that if for every integer value

n

the number

g(n)

is divisible by the number

f(n)

, then

g(x) = f(x)\cdot h(x)

, where

h(x)

is a polynomial,. Show with an example that the coefficients of the polynomial

h(x)

do not have to be integer.

Problem Statement