Properties:

1.) \(a\equiv b\) (mod \(m\)) says that \(a\) is congruent to \(b\) (mod \(m\)).

2.) Both integers \(a\) and \(b\) are congruent if and only if they have the same remainders when dividing by \(m\)

3.) If \(a\) \(\neg\equiv\) \(b\) (mod \(m\)) we can write \(a\) not congruent to \(b\) (mod \(m\)).

Addition Rule and Subtraction Rule: