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
Famous quotes containing the word extended:
“No: until I want the protection of Massachusetts to be extended to me in some distant Southern port, where my liberty is endangered, or until I am bent solely on building up an estate at home by peaceful enterprise, I can afford to refuse allegiance to Massachusetts, and her right to my property and life. It costs me less in every sense to incur the penalty of disobedience to the State than it would to obey. I should feel as if I were worth less in that case.”
—Henry David Thoreau (18171862)