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Topic: [HM] counting operations
Replies: 6   Last Post: May 20, 2000 11:38 AM

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Carlos Cesar de Araujo

Posts: 3
Registered: 12/3/04
Re: [HM] counting operations
Posted: May 8, 2000 11:05 PM
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A theorem due to the French mathematician and engineer Gabriel Lam\'e
(1795-1870) establishes an upper bound for the number of divisions
required in the Euclidean GCD algorithm. Namely, the number of
divisions required to find GCD[a,b] is less than or equal to five (5)
times the number of digits of Min[a,b]. Lam\'e's theorem appeared in

Note sur la limite du nombre des divisions, C. R. Acad. Sci. Paris
Ser. A-B 19 (1844), pp. 867-869.

It is viewed by many as the first published analysis of the ``running
time'' of a number theoretic algorithm (implying that Euclid's
algorithm runs in polynomial time).

Carlos C\e'sar de Ara\'ujo

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