Publication:
Ties in worst-case analysis of the euclidean algorithm

1

Issued Date

2021-01-01

Resource Type

Article

ISSN

13310623

Other identifier(s)

2-s2.0-85103018881

Rights

Mahidol University

Rights Holder(s)

SCOPUS

Bibliographic Citation

Mathematical Communications. Vol.26, No.1 (2021), 9-20

Suggested Citation

Brian Hopkins, Aram Tangboonduangjit Ties in worst-case analysis of the euclidean algorithm. Mathematical Communications. Vol.26, No.1 (2021), 9-20. Retrieved from: https://repository.li.mahidol.ac.th/handle/123456789/77389

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Thesis

Title

Ties in worst-case analysis of the euclidean algorithm

Author(s)

Brian Hopkins
 Aram Tangboonduangjit

Other Contributor(s)

Mahidol University
 Saint Peter’s University

Abstract

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.

Keyword(s)

Mathematics

Availability

URI

https://repository.li.mahidol.ac.th/handle/123456789/77389

Collections

Scopus 2021