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 $m$.

Sources

• 1964: Walter Ledermann: Introduction to the Theory of Finite Groups (5th ed.) ... (previous) ... (next): Chapter $\text {I}$: The Group Concept: $\S 6$: Examples of Finite Groups: $\text{(iii)}$: $(1.30)$