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:
“I do not allow myself to be moved by anything except the law. If there has been a mistake in the law, or if I think there has been perjury or injustice, I will weigh the petition most carefully, but I do not permit myself to be moved by more harrowing details, and I try to treat each case as if I was reviewing it or hearing it for the first time from the bench.”
—William Howard Taft (1857–1930)
“I had a feeling that out there, there were very poor people who didn’t have enough to eat. But they wore wonderfully colored rags and did musical numbers up and down the streets together.”
—Jill Robinson (b. 1936)