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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
Version:
Publisher's version

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Publisher copy:
10.1006/jnth.2000.2578

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Institution:
University of Oxford
Oxford college:
Wadham College
Department:
Mathematical,Physical & Life Sciences Division - Mathematical Institute
Publisher:
Elsevier B.V. Publisher's website
Journal:
Journal of Number Theory Journal website
Volume:
87
Issue:
1
Pages:
77-95
Publication date:
2001-03-05
DOI:
ISSN:
0022-314X
URN:
uuid:fc6f3446-4389-41e2-9cb4-d75505137821
Local pid:
ora:8862
Language:
English
Subjects:

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