Journal article

Markoff numbers, principal ideals and continued fraction expansions

Abstract:: Given any solution triple of natural numbers to the Markoff equation a²+b²+c²=3abc, an old problem asks whether the largest number determines the triple uniquely. We show this to be true in a range of cases by considering the factorisation of ideals in certain quadratic number fields, but also exhibit a counterexample for this approach when the question is widened to other numbers.

Publication status:: Published

Peer review status:: Peer reviewed

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APA Style

Button, J. (2001). Markoff numbers, principal ideals and continued fraction expansions. Journal of Number Theory, 87(1), 77–95.

MLA Style

Button, J. “Markoff Numbers, Principal Ideals and Continued Fraction Expansions.” Journal of Number Theory, Publisher's version, vol. 87, no. 1, 2001, pp. 77–95.

Chicago Style

Button, J. 2001. “Markoff Numbers, Principal Ideals and Continued Fraction Expansions.” Journal of Number Theory 87 (1): 77–95.
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Files:: 1-s2.0-S0022314X00925782-main.pdf

(Preview, Version of record, pdf, 151.9KB, Terms of use)

Publisher copy:: 10.1006/jnth.2000.2578

Authors

+ Button, J More by this author

Institution:: University of Oxford
Division:: MPLS
Department:: Mathematical Institute
Oxford college:: Wadham College
Role:: Author

Contributors

+ Academic Press

Role:: Other

Publisher:: Elsevier
Journal:: Journal of Number Theory More from this journal
Volume:: 87
Issue:: 1
Pages:: 77-95
Publication date:: 2001-03-01
Edition:: Publisher's version
DOI:: 10.1006/jnth.2000.2578
ISSN:: 0022-314X

Language:: English
Subjects:: Number theory

Mathematics
UUID:: uuid:fc6f3446-4389-41e2-9cb4-d75505137821
Local pid:: ora:8862
Deposit date:: 2014-08-05
ARK identifier:: ark:/29072/ora_fc6f3446438941e29cb4d75505137821

Terms of use

Copyright holder:: Academic Press
Copyright date:: 2001
Notes:: Copyright 2001 Academic Press. Published by Elsevier B.V. All rights reserved. Re-use of this article is permitted in accordance with the Terms and Conditions set out at http://www.elsevier.com/open-access/userlicense/1.0/

Licence:: Other

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