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 DivisorRelated 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