Let $\displaystyle f(x)$ be a polynomial with integral coefficients and $\displaystyle a\equiv b \ \mbox{(mod m)}$. Then $\displaystyle f(a)\equiv f(b) \ \mbox{(mod m)}$.

It make since that if a, b are in the domain, then the co-domain will also be congruent of the same integers but how do I go about doing this?