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:
“When you are invited by someone to a wedding banquet, do not sit down at the place of honor, in case someone more distinguished than you has been invited by your host...But when you are invited, go and sit down at the lowest place, so that when your host comes, he may say to you, Friend, move up higher’; then you will be honored in the presence of all who sit at the table with you.”
—Bible: New Testament, Luke 14:8,10.
“Our religion vulgarly stands on numbers of believers. Whenever the appeal is made—no matter how indirectly—to numbers, proclamation is then and there made, that religion is not. He that finds God a sweet, enveloping presence, who shall dare to come in?”
—Ralph Waldo Emerson (1803–1882)