# Category:Modulo Arithmetic

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This category contains results about Modulo Arithmetic.

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

**Modulo arithmetic** is the branch of abstract algebra which studies the residue class of integers under a modulus.

As such it can also be considered to be a branch of number theory.

## Subcategories

This category has the following 19 subcategories, out of 19 total.

### A

### C

### E

### I

### M

### P

### R

### S

### W

## Pages in category "Modulo Arithmetic"

The following 70 pages are in this category, out of 70 total.

### C

- Cancellability of Congruences
- Canonical Epimorphism from Integers by Principal Ideal
- Chinese Remainder Theorem
- Chinese Remainder Theorem/Warning
- Common Factor Cancelling in Congruence
- Congruence by Divisor of Modulus
- Congruence by Divisor of Modulus/Integer Modulus
- Congruence by Product of Moduli
- Congruence by Product of Moduli/Real Modulus
- Congruence Modulo Integer is Equivalence Relation
- Congruence Modulo Negative Number
- Congruence Modulo Real Number is Equivalence Relation
- Congruence Modulo Zero is Diagonal Relation
- Congruence of Powers
- Congruence of Product
- Congruence of Quotient
- Congruent Integers less than Half Modulus are Equal
- Congruent Numbers are not necessarily Equal
- Congruent to Zero if Modulo is Divisor
- Cube Modulo 9

### E

### F

### I

- Integer Coprime to Modulus iff Linear Congruence to 1 exists
- Integer Coprime to Modulus iff Linear Congruence to 1 exists/Corollary
- Integer has Multiplicative Order Modulo n iff Coprime to n
- Integer is Congruent Modulo Divisor to Remainder
- Integer is Congruent Modulo Divisor to Remainder/Corollary
- Integer is Congruent to Integer less than Modulus
- Integer of form 6k + 5 is of form 3k + 2 but not Conversely
- Integer to Power of p-1 over 2 Modulo p
- Intersection of Congruence Classes

### L

### M

### N

### P

### R

### S

- Solution of Linear Congruence
- Solution to Simultaneous Linear Congruences
- Solutions of Polynomial Congruences
- Square Modulo 3
- Square Modulo 4
- Square Modulo 5
- Square Modulo 5/Corollary
- Square Modulo 8
- Square Modulo n Congruent to Square of Inverse Modulo n
- Square of Modulo less One equals One
- Sufficient Condition for 5 to divide n^2+1