Reduced Residue System/Examples/Modulo 18/Arithmetic Sequence

Examples of Reduced Residue Systems
The arithmetic sequence:


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

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

Proof
We have:

Thus we see that:
 * $\set {5, 11, 17, 23, 29, 35}$

is equivalent to:
 * $\set {1, 5, 17}$

While $\set {1, 5, 17}$ are all coprime to $18$, they do not form a least positive reduced residue system modulo $18$, which is:


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

from Least Positive Reduced Residue System Modulo 18.