Simultaneous congruence

In number theory, a simultaneous congruence describes a system of linear congruences

${\displaystyle {\begin{matrix}x&\equiv &a_{1}&\mod m_{1}\\x&\equiv &a_{2}&\mod m_{2}\\&\vdots &&\\x&\equiv &a_{n}&\mod m_{n}\\\end{matrix}}}$

for which all x are to be determined that solve all congruences at the same time. There can be, but does not have to be, a clear solution.

Simultaneous congruences can be solved with the Chinese remainder of the sentence or by means of successive substitutions .