Complete Residue System/Examples/Modulo 11/Powers of 2

Examples of Complete Residue Systems
The set of integers:


 * $\set {0, 1, 2, 4, 8, 16, 32, 64, 128, 256, 512}$

forms a complete residue system modulo $11$.

Proof
We have:

Thus we see that:
 * $\set {0, 1, 2, 4, 8, 16, 32, 64, 128, 256, 512}$

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

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