Extended Euclidean Algorithm

The extended Euclidean algorithm is an extension to the Euclidean algorithm. Besides finding the greatest common divisor of integers a and b, as the Euclidean algorithm does, it also finds integers x and y (one of which is typically negative) that satisfy Bézout's identity

The extended Euclidean algorithm is particularly useful when a and b are coprime, since x is the multiplicative inverse of a modulo b, and y is the multiplicative inverse of b modulo a.

Read more about Extended Euclidean Algorithm:  Informal Formulation of The Algorithm, Computing A Multiplicative Inverse in A Finite Field, The Case of More Than Two Numbers

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