The extended greatest common divisor of two integers
and
can be defined as the greatest common divisor of and which also satisfies the constraint for and given integers. It is used in
solving linear Diophantine equations, and
is implemented in the Wolfram Language
as `ExtendedGCD`[*m*,
*n*].

# Extended Greatest Common Divisor

## See also

Greatest Common Divisor## Related Wolfram sites

http://functions.wolfram.com/IntegerFunctions/ExtendedGCD/## Explore with Wolfram|Alpha

## Cite this as:

Weisstein, Eric W. "Extended Greatest Common Divisor." From *MathWorld*--A Wolfram Web Resource. https://mathworld.wolfram.com/ExtendedGreatestCommonDivisor.html