Extended Euclidean Algorithm - The Case of More Than Two Numbers

The Case of More Than Two Numbers

One can handle the case of more than two numbers iteratively. First we show that . To prove this let . By definition of gcd is a divisor of and . Thus for some . Similarly is a divisor of so for some . Let . By our construction of, but since is the greatest divisor is a unit. And since the result is proven.

So if then there are and such that so the final equation will be

So then to apply to n numbers we use induction

with the equations following directly.

Read more about this topic:  Extended Euclidean Algorithm

Famous quotes containing the words case and/or numbers:

    Stella, take these binoculars out of the case and bring them here, will ya? Trouble. I can smell it.
    John Michael Hayes (b. 1919)

    He bundles every forkful in its place,
    And tags and numbers it for future reference,
    So he can find and easily dislodge it
    In the unloading. Silas does that well.
    He takes it out in bunches like birds’ nests.
    Robert Frost (1874–1963)