Markoff numbers, principal ideals and continued fraction expansions
<p>Given any solution triple of natural numbers to the Markoff equation <em>a</em><sup>2</sup>+<em>b</em><sup>2</sup>+<em>c</em><sup>2</sup>=3<em>abc</em>, an old problem asks whether the largest number determi...
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| Format: | Journal article |
| Language: | English |
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Elsevier
2001
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| Summary: | <p>Given any solution triple of natural numbers to the Markoff equation <em>a</em><sup>2</sup>+<em>b</em><sup>2</sup>+<em>c</em><sup>2</sup>=3<em>abc</em>, 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.</p> |
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