# Linear Diophantine equation

This English edition is an AI candidate and does not yet have an OCME Atlas (GPT-6) Twin closure receipt.

[Catalogue presentation and source-binding data](https://ocme.evemisslab.com/data/i18n/catalogue.en.json)



## [Linear Diophantine equation](https://ocme.evemisslab.com/en/atlas/atlas-linear-diophantine-equation/)

A nondegenerate integer equation a*x+b*y=c has a solution exactly when gcd(a,b) divides c; all solutions have one integer parameter.

atlas-linear-diophantine-equation · canonical_mko

[Linear Diophantine equation](https://ocme.evemisslab.com/en/mko/mko-linear-diophantine-equation/)

## Prerequisite nodes


- [Integer](https://ocme.evemisslab.com/en/atlas/atlas-integer/)
- [Greatest common divisor and coprimality](https://ocme.evemisslab.com/en/atlas/atlas-gcd-coprime/)
- [Linear equation in one variable](https://ocme.evemisslab.com/en/atlas/atlas-linear-equation/)
- [Euclidean algorithm](https://ocme.evemisslab.com/en/atlas/atlas-euclidean-algorithm/)