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:
“While the light burning within may have been divine, the outer case of the lamp was assuredly cheap enough. Whitman was, from first to last, a boorish, awkward poseur.”
—Rebecca Harding Davis (1831–1910)
“Green grow the rushes-O
What is your one-O?”
—Unknown. Carol of the Numbers (l. 2–3)