Definition:Simultaneous Congruences/Solution
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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:
- 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.