Complete Residue System/Examples/Modulo 11

Examples of Complete Residue Systems

Powers of $2$

The set of integers:

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

forms a complete residue system modulo $11$.

Odd Integers

The set of integers:

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

forms a complete residue system modulo $11$.

Even Integers

The set of integers:

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

forms a complete residue system modulo $11$.

Least Absolute Residues

The set of integers:

$\set {-5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5}$

forms a complete residue system modulo $11$.