Definition:Reduced Residue System/Least Positive
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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: $\text{(iii)}$: $(1.30)$