@article{oai:teapot.lib.ocha.ac.jp:00034622,
author = {Hosoya, Haruo},
issue = {2},
journal = {お茶の水女子大學自然科學報告},
month = {Jan},
note = {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.},
pages = {19--33},
title = {Pell Equation. II. Mathematical structure of the family of the solutions of the Pell equation},
volume = {57},
year = {2007}
}