Reduced Residue System/Examples/Modulo 18

Examples of Reduced Residue Systems

Least Positive Residues

The least positive reduced residue system of $18$ is the set of positive integers:

$\set {1, 5, 7, 11, 13, 17}$

Powers of $5$

The set of integers:

$\set {1, 5, 25, 125, 625, 3125}$

forms a reduced residue system modulo $18$.

Arithmetic Sequence

The arithmetic sequence:

$\set {5, 11, 17, 23, 29, 35}$

does not form a reduced residue system modulo $18$.

Square Numbers

The set of integers:

$\set {1, 25, 49, 121, 169, 289}$

does not form a reduced residue system modulo $18$.