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:
“The attention of those who frequent the camp-meetings at Eastham is said to be divided between the preaching of the Methodists and the preaching of the billows on the back side of the Cape, for they all stream over here in the course of their stay. I trust that in this case the loudest voice carries it. With what effect may we suppose the ocean to say, “My hearers!” to the multitude on the bank. On that side some John N. Maffit; on this, the Reverend Poluphloisboios Thalassa.”
—Henry David Thoreau (1817–1862)
“All ye poets of the age,
All ye witlings of the stage,
Learn your jingles to reform,
Crop your numbers to conform.
Let your little verses flow
Gently, sweetly, row by row;
Let the verse the subject fit,
Little subject, little wit.
Namby-Pamby is your guide,
Albion’s joy, Hibernia’s pride.”
—Henry Carey (1693?–1743)