Complete Residue System/Examples/Modulo 11/Even Integers

Examples of Complete Residue Systems
The set of integers:


 * $\set {2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22}$

forms a complete residue system modulo $11$.

Proof
We have:

Thus we see that:
 * $\set {2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22}$

is equivalent to:
 * $\set {2, 4, 6, 8, 10, 1, 3, 5, 7, 9, 0}$

The result follows from Initial Segment of Natural Numbers forms Complete Residue System.