MathDB

Let

f{}

and

g{}

be polynomials with integers coefficients. The leading coefficient of

g{}

is equal to 1. It is known that for infinitely many natural numbers

n{}

the number

f(n)

is divisible by

g(n)

. Prove that

f(n)

is divisible by

g(n)

for all positive integers

n{}

such that

g(n)\neq 0

.
From the folklore

Problem Statement