Pell Equation. II. Mathematical structure of the family of the solutions of the Pell equation
Bibliographic Information
- Other Title
-
- Pell equation 2 Mathematical structure of the family of the solutions of the Pell equation
Search this article
Abstract
application/pdf
紀要論文
Mathematical structure of the families of solutions of Pell equations x^2-Dy^2=1 (called Pell-1) and x^2-Dy^2=-1 (Llep-1) are studied by using Cayley-Hamilton theorem. Besides discovery of several new recursive relations, it was found that the solutions (x_n, y_n) of Pell-1 are expressed by the Chebyshev polynomials of the first and second kinds, T_n and U_n, in terms of the smallest solutions (x_1, y_1). The solutions (t_n, u_n) of Pellep-1 which are the combination of Pell-1 and Llep-1 are expressed by using the conjugate Chebyshev polynomials. Similar results are obtained for the solutions of Pellep-4 through the modified Chebyshev polynomials and their conjugates. The solutions of Pellep-4 with several D values are found to form various interesting mathematical series of numbers, such as Fibonacci, Lucas, Pell numbers.
Journal
-
- お茶の水女子大學自然科學報告
-
お茶の水女子大學自然科學報告 57 (2), 19-33, 2007-01
お茶の水女子大学
- Tweet
Details 詳細情報について
-
- CRID
- 1050282677927361920
-
- NII Article ID
- 110006559635
-
- NII Book ID
- AN00033958
-
- ISSN
- 00298190
-
- HANDLE
- 10083/2403
-
- NDL BIB ID
- 8785053
-
- Text Lang
- en
-
- Article Type
- departmental bulletin paper
-
- Data Source
-
- IRDB
- NDL
- CiNii Articles