# Category:Reduced Residue Systems

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This category contains results about Reduced Residue Systems.

Definitions specific to this category can be found in Definitions/Reduced Residue Systems.

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 $m$.

## Subcategories

This category has the following 3 subcategories, out of 3 total.

### E

### M

### R

## Pages in category "Reduced Residue Systems"

The following 6 pages are in this category, out of 6 total.