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:
“God ... created a number of possibilities in case some of his prototypes failed—that is the meaning of evolution.”
—Graham Greene (1904–1991)
“What culture lacks is the taste for anonymous, innumerable germination. Culture is smitten with counting and measuring; it feels out of place and uncomfortable with the innumerable; its efforts tend, on the contrary, to limit the numbers in all domains; it tries to count on its fingers.”
—Jean Dubuffet (1901–1985)