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Math Help - Polynomial Congruence Proof

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    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).
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    Quote Originally Posted by erictorius View Post
    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?
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