The extended greatest common divisor of two integers 
and 
consists of their greatest common divisor 
together with integers 
and 
satisfying 
. The coefficients 
and 
are computed by the extended Euclidean
algorithm. The extended greatest common divisor is used in solving linear Diophantine equations, and is implemented in
the Wolfram Language as ExtendedGCD[m,
n].
Extended Greatest Common Divisor
See also
Bézout's Identity, Extended Euclidean Algorithm, Greatest Common DivisorRelated Wolfram sites
https://functions.wolfram.com/IntegerFunctions/ExtendedGCD/Explore with Wolfram|Alpha
Cite this as:
Weisstein, Eric W. "Extended Greatest Common Divisor." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/ExtendedGreatestCommonDivisor.html