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So far we have seen how to add, subtract and multiply with congruences. What about division? There is a reason we have waited to discuss it. It turns out that we cannot simply divide. In other words, even if \(ad \equiv bd \pmod n\text{,}\) we do not know that \(a \equiv b \pmod n\text{.}\) Consider, for example:

\begin{equation*} 18 \equiv 42 \pmod 8\text{.} \end{equation*}

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