# Category:Modulo Addition

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This category contains results about **Modulo Addition**.

Definitions specific to this category can be found in Definitions/Modulo Addition.

Let $m \in \Z$ be an integer.

Let $\Z_m$ be the set of integers modulo $m$:

- $\Z_m = \set {\eqclass 0 m, \eqclass 1 m, \ldots, \eqclass {m - 1} m}$

where $\eqclass x m$ is the residue class of $x$ modulo $m$.

The operation of **addition modulo $m$** is defined on $\Z_m$ as:

- $\eqclass a m +_m \eqclass b m = \eqclass {a + b} m$

## Subcategories

This category has the following 2 subcategories, out of 2 total.

### M

- Modulo Subtraction (1 P)

## Pages in category "Modulo Addition"

The following 20 pages are in this category, out of 20 total.

### I

### M

- Modulo Addition has Identity
- Modulo Addition has Inverses
- Modulo Addition is Associative
- Modulo Addition is Closed
- Modulo Addition is Closed/Integers
- Modulo Addition is Closed/Real Numbers
- Modulo Addition is Commutative
- Modulo Addition is Linear
- Modulo Addition is Well-Defined
- Modulo Addition is Well-Defined/Real Modulus
- Modulo Addition/Cayley Table
- Modulo Multiplication Distributes over Modulo Addition
- Modulo Subtraction is Well-Defined