Algorithm and bound for the greatest common divisor of n integers-Reference-Cited by-同舟云学术

Algorithm and bound for the greatest common divisor of n integers

Published:1970-07 Issue:7 Volume:13 Page:433-436
ISSN:0001-0782
Container-title:Communications of the ACM
language:en
Short-container-title:Commun. ACM

Author:

Bradley Gordon H.¹

Affiliation:

1. Yale Univ., New Haven, CT

Abstract

A new version of the Euclidean algorithm for finding the greatest common divisor of n integers a i and multipliers x i such that gcd = x 1 a 1 + ··· + x n a n is presented. The number of arithmetic operations and the number of storage locations are linear in n . A theorem of Lamé that gives a bound for the number of iterations of the Euclidean algorithm for two integers is extended to the case of n integers. An algorithm to construct a minimal set of multipliers is presented. A Fortran program for the algorithm appears as Comm. ACM Algorithm 386.

Publisher

Association for Computing Machinery (ACM)

Subject

General Computer Science

Link

https://dl.acm.org/doi/pdf/10.1145/362686.362694

Reference8 articles.

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3. Note sur la limite du nombre des divisions dans la recherche du plus grand comrnun diviseur entre deux hombres entiers;LAME G;C. R. Acad. Sci. Paris,1844

4. A Minimum Solution of a Diophantine Equation

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