Definition:Reduced Residue System/Least Positive

Definition
Let $m \in \Z_{> 0}$. The least positive reduced residue system modulo $m$ is the set of integers:
 * $\set {a_1, a_2, \ldots, a_{\map \phi m} }$

with the following properties:
 * $\map \phi m$ is the Euler $\phi$ function
 * $\forall i: 0 < a_i < m$
 * each of which is prime to $m$
 * no two of which are congruent modulo $m$.

Also known as
The least positive reduced residue system modulo $m$ is also referred to as the set of least positive coprime residues modulo $m$.