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## Homework Statement

Let m be a positive integer. Show that a mod m = b mod m if [itex]a\,\equiv\,b\left(mod\,m\right)[/itex].

## Homework Equations

Congruency - [tex]a\,\equiv\,b\left(mod\,m\right)[/tex]

a is congruent to b modulo m.

## The Attempt at a Solution

I really, really, really suck at proofs. But here is what I tried.

[tex]a\,\equiv\,b\left(mod\,m\right)\,\longrightarrow\,a\,mod\,m\,\equiv\,\left[b\left(mod\,m\right)\right]\,\left(mod\,m\right)[/tex]

I have no idea how to prove

**about this stuff. Please help!!!**

__anything__