Definition:Reduced Residue System/Least Positive

Definition
Let $m \in \Z_{> 0}$. The least positive coprime residues modulo $m$ is a set of integers:
 * $\left\{{a_1, a_2, \ldots, a_{\phi \left({m}\right)}}\right\}$

with the following properties:
 * $\phi \left({m}\right)$ 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.