# Category:Coprime Integers

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This category contains results about integers which are coprime.

Definitions specific to this category can be found in Definitions/Coprime Integers.

Let $a$ and $b$ be integers such that $b \ne 0$ and $a \ne 0$ (that is, they are both non-zero).

Let $\gcd \set {a, b}$ denote the greatest common divisor of $a$ and $b$.

Then $a$ and $b$ are **coprime** if and only if $\gcd \set {a, b} = 1$.

## Subcategories

This category has the following 8 subcategories, out of 8 total.

### C

### E

### G

### I

### P

## Pages in category "Coprime Integers"

The following 41 pages are in this category, out of 41 total.

### C

### D

### I

- Integer Combination of Coprime Integers
- Integer Coprime to all Factors is Coprime to Whole
- Integer Coprime to all Factors is Coprime to Whole/Proof 1
- Integer has Multiplicative Order Modulo n iff Coprime to n
- Integer is Coprime to 1
- Integers are Coprime iff Powers are Coprime
- Integers Coprime to Zero
- Integers Divided by GCD are Coprime

### N

### P

- Power of Generator of Cyclic Group is Generator iff Power is Coprime with Order
- Powers of Coprime Numbers are Coprime
- Prime iff Coprime to all Smaller Positive Integers
- Prime not Divisor implies Coprime
- Probability of Three Random Integers having no Common Divisor
- Probability of Two Random Integers having no Common Divisor
- Product of Coprime Factors
- Product of Coprime Numbers whose Sigma is Square has Square Sigma
- Product of Coprime Pairs is Coprime