Symbols:Z/Reduced Residue System
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Reduced Residue System Modulo $m$
- $\Z'_m$
The reduced residue system modulo $m$, denoted $\Z'_m$, is the set of all residue classes of $k$ (modulo $m$) which are prime to $m$:
- $\Z'_m = \set {\eqclass k m \in \Z_m: k \perp m}$
Thus $\Z'_m$ is the set of all coprime residue classes modulo $m$:
- $\Z'_m = \set {\eqclass {a_1} m, \eqclass {a_2} m, \ldots, \eqclass {a_{\map \phi m} } m}$
where:
- $\forall k: a_k \perp m$
- $\map \phi m$ denotes the Euler phi function of $m$.
The $\LaTeX$ code for \(\Z'_m\) is \Z'_m
or \mathbb Z'_m
or \Bbb Z'_m
.