Diophantine equations and class numbers of real quadratic fields (Q2717603)
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scientific article; zbMATH DE number 1605201
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Diophantine equations and class numbers of real quadratic fields |
scientific article; zbMATH DE number 1605201 |
Statements
Diophantine equations and class numbers of real quadratic fields (English)
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17 June 2001
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real quadratic field
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class number
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Pell's equation
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higher degree Diophantine equation
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Lucas sequence
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cryptographic problem
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convergent
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divisibility
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0.96809614
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0.9596055
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0.95799375
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0.9570138
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0.9557618
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0.9553496
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Let \(d\) be a positive integer that is square free, and let \(h(d)\) denote the class number of the real quadratic field \(\mathbb{Q}(\sqrt{d})\). In the present paper the authors give some results concerning the divisibility of \(h(d)\) while \(d\) satisfies \(da^2= 1+4b^2 k^{2n}\), where \(a,b,k,n\) are positive integers satisfying \(k>1\) and \(n>1\).
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