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 the case, case and/or numbers:
“Chile consents to do all we can reasonably demand. My regret is that our Government blustered and bullied. President [Benjamin] Harrison argued in his message like a prosecutor—made the most of the case against our weak sister. Forbearance, charity, friendship, arbitration should have been in our words and thoughts.”
—Rutherford Birchard Hayes (1822–1893)
“I’m a very smart guy. I haven’t a feeling or a scruple in the world. All I have the itch for is money. I am so money greedy that for twenty-five bucks a day and expenses, mostly gasoline and whisky, I do my thinking myself, what there is of it; I risk my whole future, the hatred of the cops ... I dodge bullets and eat saps, and say thank you very much, if you have any more trouble, I hope you’ll think of me, I’ll just leave one of my cards in case anything comes up.”
—Raymond Chandler (1888–1959)
“I’m not even thinking straight any more. Numbers buzz in my head like wasps.”
—Kurt Neumann (1906–1958)