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 am absurdly fearful about this voyage. Various little omens have combined to give me a dark feeling.... Perhaps we shall live to laugh at these. But in case of mishap I should perish with my husband and child, perhaps to be transferred to some happier state.”
—Margaret Fuller (1810–1850)
“Out of the darkness where Philomela sat,
Her fairy numbers issued. What then ailed me?
My ears are called capacious but they failed me,
Her classics registered a little flat!
I rose, and venomously spat.”
—John Crowe Ransom (1888–1974)