Congruence and Divisibility.
For any integers \(a\text{,}\) \(b\text{,}\) and \(n\text{,}\) we have
\begin{equation*}
a \equiv b \pmod{n} \qquad \text{ if and only if } \qquad n \mid a-b\text{.}
\end{equation*}
For any integers \(a\text{,}\) \(b\text{,}\) and \(n\text{,}\) we have