The Euclidean Algorithm and the Linear Diophantine Equation ax plus by = gcd(a, b)

被引：2
|
作者：
Rankin, S. A. [1 ]
机构：
[1] Univ Western Ontario, Dept Math, London, ON N6A 5B7, Canada
来源：
AMERICAN MATHEMATICAL MONTHLY | 2013年 / 120卷 / 06期
关键词：
D O I：
10.4169/amer.math.monthly.120.06.562
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this note, we prove that for any positive integers a and b, with d = gcd(a, b), among all integral solutions to the equation ax + by = d, the solution (x(0), y(0)) that is provided by the Euclidean algorithm lies nearest to the origin. In fact, we prove that (x(0), y(0)) lies in the interior of the circle centered at the origin with radius 1/2d root a(2) + b(2).
引用
收藏
页码：562 / 564
页数：3
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