2024-03-29T14:54:53Z
https://teapot.lib.ocha.ac.jp/oai
oai:teapot.lib.ocha.ac.jp:00034630
2022-12-12T05:38:58Z
347:359:683
Pell Equation. I. Systematic classification of the solutions of the Pell equation
Hosoya, Haruo
70902
Asamoto, Noriko
70903
400
application/pdf
紀要論文
Let the smallest non-trivial solution of Pell equation, x^2-Dy^2=1, be denoted by (x_1, y_1). The Pell equations for D were systematically classified into several types with respect to the form of the polynomial relations (PR's) among (D, x_1, y_1). The key strategies for this analysis are the value of y_1 and form of the continued fraction expansion of √<D>. Among the solutions of Pell equation with D below 100 only four D's were found to have no other D below ten thousand connected through a PR. All the PR's were shown to be derived from a pair of the "master equations". The results obtained in this paper show an effectiveness of the proposed strategies for the systematic analysis of the chaotic behavior of the solutions of Pell equation.
departmental bulletin paper
お茶の水女子大学
2006-09
application/pdf
お茶の水女子大學自然科學報告
1
57
57
83
AN00033958
00298190
https://teapot.lib.ocha.ac.jp/record/34630/files/KJ00004830808.pdf
eng