\begin{definition}[Definition:Reduced Residue System/Least Positive]
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 $m$.
\end{definition}