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 Congruence: if one such element of a congruence class satisfies the congruences, they all do.

Also see

• Results about simultaneous congruences can be found here.