Definition:Complete Residue System

Definition
Let $m \in \Z_{\ne 0}$ be a non-zero integer.

Let $S := \set {r_1, r_2, \dotsb, r_s}$ be a set of integers with the properties that:


 * $(1): \quad i \ne j \implies r_i \not \equiv r_j \pmod m$


 * $(2): \quad \forall n \in \Z: \exists r_i \in S: n \equiv r_i \pmod m$

Then $S$ is a complete residue system modulo $m$.

Also see

 * Definition:Residue (Modulo Arithmetic)


 * Definition:Residue Class
 * Definition:Set of Residue Classes


 * Definition:Reduced Residue System