Definition:Reduced Residue System/Least Positive

Definition
Let $$n \in \Z: n \ge 1$$.

Let $$\phi \left({n}\right)$$ be the Euler phi function of $$n$$.

The reduced residue system modulo $$n$$ is a set of integers:
 * $$\left\{{a_1, a_2, \ldots, a_{\phi \left({n}\right)}}\right\}$$

with the following properties:
 * each of which is prime to $$n$$;
 * no two of which are congruent modulo n.

Also known as a reduced set of residues modulo $$n$$.

Least Positive Residues
If each element of $$\left\{{a_1, a_2, \ldots, a_{\phi \left({n}\right)}}\right\}$$ is a positive integer less than or equal to $$n$$, this is called the reduced set of least positive residues modulo $$n$$.

Examples
The reduced set of least positive residues modulo $$n$$ for the first few integers are:

$$ $$ $$ $$ $$ $$ $$ $$ $$ $$