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

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