2020-05-29T12:52:39Zhttps://teapot.lib.ocha.ac.jp/?action=repository_oaipmhoai:teapot.lib.ocha.ac.jp:000346222020-04-21T01:16:31Z00347:00359:00684
Pell Equation. II. Mathematical structure of the family of the solutions of the Pell equationenghttp://hdl.handle.net/10083/2403Departmental Bulletin PaperHosoya, HaruoMathematical 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.お茶の水女子大學自然科學報告57219332007-0100298190AN00033958application/pdf400https://teapot.lib.ocha.ac.jp/?action=repository_action_common_download&item_id=34622&item_no=1&attribute_id=21&file_no=1お茶の水女子大学紀要論文2018-03-19