Definition:Simultaneous Congruences/Solution

Definition
A solution of a system of simultaneous congruences is a residue class modulo $\lcm \set {n_1, n_2, \ldots, n_r}$ such that any element of that class satisfies all the congruences.

Also see
For conditions under which this solution exists:


 * Chinese Remainder Theorem
 * Solution to Simultaneous Linear Congruences


 * Solutions of Polynomial Congruences: if one such element of a congruence class satisfies the congruences, they all do.