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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### Famous quotes containing the word extended:

“Whenever there are in any country uncultivated lands and unemployed poor, it is clear that the laws of property have been so far *extended* as to violate natural right. The earth is given as a common stock for man to labor and live on.... The small landowners are the most precious part of a state.”

—Thomas Jefferson (1743–1826)