# Math Help - Polynomial Congruence Proof

1. ## Polynomial Congruence Proof

I'm having some difficulty coming up with a sufficient proof to the following problem. Any help would be appreciated.

Let f(x) be a polynomial of degree at least 1 with integer coefficients. Prove that if f(x0)= m, m>0, then f(x) is congruent to 0 (mod m) for all x congruent to x0 (mod m).

2. Originally Posted by erictorius
I'm having some difficulty coming up with a sufficient proof to the following problem. Any help would be appreciated.

Let f(x) be a polynomial of degree at least 1 with integer coefficients. Prove that if f(x0)= m, m>0, then f(x) is congruent to 0 (mod m) for all x congruent to x0 (mod m).
If $a\equiv b(\bmod m) \implies a^n \equiv b^n (\bmod m)$.
Can you use this hint to finish the problem?