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Suppose \(a \equiv b \pmod{n}\) and \(c \equiv d \pmod{n}\text{.}\) That means \(a = b + kn\) and \(c = d + jn\) for integers \(k\) and \(j\text{.}\) Add these equations:

\begin{equation*} a+c = b+d + kn + jn\text{.} \end{equation*}

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