Systems of Linear Congruences

You can reduce systems of any number of congruences to a single congruence by solving systems of congruences two at a time. The Chinese remainder theorem states that, if the moduli are relatively prime in pairs, then there is a unique solution modulo the product of all the moduli.



\begin{example}
Consider the
\index{Systems of congruences@Systems of congrue...
...13320867\left( \limfunc{mod}\,51935469\right)
\end{displaymath}
\end{example}