Ties in Worst-Case Analysis of the Euclidean Algorithm

被引：0

作者：

Hopkins, Brian ^{[1
]}

Tangboonduangjit, Aram ^{[2
]}

机构：

[1] St Peters Univ, 2641 John F Kennedy Blvd, Jersey City, NJ 07306 USA

[2] Mahidol Univ Int Coll, 999 Phutthamonthon Sai 4 Rd, Phutthamonthon Dist 73170, Nakhon Pathom, Thailand

来源：

MATHEMATICAL COMMUNICATIONS | 2021年 / 26卷 / 01期

关键词：

Euclidean algorithm; continuant polynomials; Fibonacci numbers;

D O I：

暂无

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We determine all pairs of positive integers below a given bound that require the most steps in the Euclidean algorithm. Also, we find asymptotic probabilities for a unique maximum pair or an even number of them. Our primary tools are continuant polynomials and the Zeckendorf representation using Fibonacci numbers.

引用

页码：9 / 20

页数：12

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