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Assume \(a \equiv b \pmod n\) and \(c \equiv d \pmod n\text{.}\) This means \(a = b + kn\) and \(c = d + jn\) for some integers \(k\) and \(j\text{.}\) Consider \(a-c\text{.}\) We have:

\begin{equation*} a-c = b+kn - (d+jn) = b-d + (k-j)n\text{.} \end{equation*}

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