Pell Equation. V. Systematic relation between the Pythagorean triples and Pell equations
Bibliographic Information
- Other Title
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- Pell equation 5 Systematic relation between the Pythagorean triples and Pell equations
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Abstract
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紀要論文
Systematic relations between the algebra of the Pell equations, x^2 - Dy^2 = 1 (called Pell-1) and x^2 - Dy^2 = -1 (called Llep-1), and the geometry of Pythagorean triangles or Pythagorean triples (PTs) are discussed. Although Llep-1 is solvable only for a limited number (though extending to infinity) of D values, such an algorithm is obtained that can construct a series of PTs corresponding to each D and involving rational number approximation of the square root of D. In the case of Pell-1, which is solvable for all square-free D, a simple algorithm is found for odd D, whereas some modification is necessary for even D. For each series of PTs thus obtained interesting properties regarding their recursive relations are found.
Journal
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- お茶の水女子大學自然科學報告
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お茶の水女子大學自然科學報告 59 (1), 19-34, 2008-08
お茶の水女子大学
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Details 詳細情報について
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- CRID
- 1050282677924271744
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- NII Article ID
- 110007150528
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- NII Book ID
- AN00033958
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- ISSN
- 00298190
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- HANDLE
- 10083/35237
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- NDL BIB ID
- 10254228
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- Text Lang
- en
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- Article Type
- departmental bulletin paper
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- Data Source
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- IRDB
- NDL
- CiNii Articles