Markoff numbers, principal ideals and continued fraction expansions (Q5931956)
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scientific article; zbMATH DE number 1594762
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Markoff numbers, principal ideals and continued fraction expansions |
scientific article; zbMATH DE number 1594762 |
Statements
Markoff numbers, principal ideals and continued fraction expansions (English)
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23 April 2002
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principal ideals
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continued fractions
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Markoff triple
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Markoff number
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0.8892566
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0.88595676
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0.88310933
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0.87744296
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0.87367666
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0.8712966
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0.8701186
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0.8676487
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A Markoff triple is a triple \((a,b,c)\) of natural numbers solving the Markoff equation NEWLINE\[NEWLINEa^2+ b^2+ c^2= 3abc,NEWLINE\]NEWLINE and a Markoff number is the largest number in a Markoff triple. It is an old problem whether the Markoff number determines the triple uniquely. This problem has an affirmative answer in certain cases using the factorization of ideals in quadratic number fields.
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