##  [Bézout's Identity](/bezouts-identity) 

  ##  [Bézout's Identity](https://algebra.quantumdictionary.io/bezouts-identity-0) 

  

 [![Algebra](/sites/default/files/styles/large/public/2026-01/Algebra.png.webp?itok=3pHxBnUF)](/topic-specific-dictionaries/pure-mathematics/algebra)

- Pure Mathematics -

**Algebra Dictionary**

 







 

 

 

 



 

 

 

 

Definition

The statement that for any integers a and b not both zero there exist integers x and y such that gcd(a,b) = ax + by; that is, the greatest common divisor can be expressed as an integer linear combination of a and b.