Talk:Euclidean algorithm

Article Checklist for "Euclidean algorithm"

Workgroup category or categories	Mathematics Workgroup [Categories OK]
Article status	Developing article: beyond a stub, but incomplete
Underlinked article?	No
Basic cleanup done?	Yes
Checklist last edited by	Catherine Woodgold

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It says "Since one cannot go on getting smaller and smaller positive integers forever, one must reach a point where one of the two is 0." This seems to imply that 0 is a positive integer (or the proof isn't quite rigourous or something; if 0 is allowed, maybe other things that are not positive integers are allowed so one can't use well-ordering? Just a minor point that needs to be cleaned up in the wording, though I don't immediately see a good way to do it.)

Another problem: It is implied here but not stated (and it is true, and is stated on the Greatest common divisor page) that the last number found before 0 is the gcd (rather than being a larger number divisible by the gcd), but no proof is given for this. I think there's a simple inductive proof working backwards from the end of the algorithm. --Catherine Woodgold 08:36, 13 May 2007 (CDT)