We can add congruences: Notice that if \(a\equiv b\) (mod \(m\)) and \(c\equiv d\) (mod \(m\)), then \(a+c\equiv c+d\) (mod \(m\)).

We can multiply congruences: Notice that if \(a\equiv b\) (mod \(m\)) and \(c\equiv d\) (mod \(m\)), then \(ac\equiv bd\) (mod \(m\)).

Power theorem: When multiplying \(a\equiv b\) to itself numerous times, we get \(a^n\equiv b^n\) (mod \(m\)) when data-equation="n\ge0.">\(n\ge0.\)