Complete Residue System/Examples/Modulo 11/Odd Integers

Examples of Complete Residue Systems
The set of integers:


 * $\set {1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21}$

forms a complete residue system modulo $11$.

Proof
We have:

Thus we see that:
 * $\set {1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21}$

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

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