MathDB

Let

n{}

be a natural number and

f{}

be polynomial with integer coefficients. It is known that for any integer

m{}

there is an integer

k{}

such that

f(k)-m

is divisible by

n{}

. Prove that there exists a polynomial

g{}

with integer coefficients such that

f(g(m))-m

is divisible by

n{}

for any integer

m{}

.
From the folklore

Problem Statement