Coprime integers

Definition

Two integers $a$ and $b$ are coprime when their greatest common divisor is $1$ , that is, when $\gcd(a, b) = 1$ .

Remarks

Equivalently, $a$ and $b$ are coprime when the only integers that divide both of them are $1$ and $-1$ . For example, $8$ and $15$ are coprime, but $8$ and $12$ are not, because $4$ divides both. The integers $1$ and $-1$ are coprime to each integer. The integer $0$ is coprime only to $1$ and $-1$ . By Bézout's identity, $a$ and $b$ are coprime if and only if $a x + b y = 1$ for some integers $x$ and $y$ .

Reading path

To understand this page from the ground up, read these 3 pages in order. The foundations come first.

Show the path as a graph

Each page uses the pages above it. The colour of the bar on a box shows how strong the evidence is, and the box also gives it as text. The list has the same pages.

no evidence level

Divisibility definition
Greatest common divisor definition
Coprime integers definition

Where this leads

42 pages build on this one.

Tag	`0GFKP8F8AG`
URI	`m2://0GFKP8F8AG`
Aliases	`relatively-prime`, `mutually-prime`
Kind	definition
Writing	W1 stated
MSC	11A05
Defines	Coprime integers
Uses	Greatest common divisor

Coprime integers

Definition

Remarks

Reading path

Where this leads

Further reading

What this page needs for W2

What links here

Used by