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.
雑誌名
お茶の水女子大學自然科學報告
巻
57
号
1
ページ
57 - 83
発行年
2006-09
ISSN
00298190
書誌レコードID
AN00033958
フォーマット
application/pdf
形態
1189700 bytes
日本十進分類法
400
出版者
お茶の水女子大学
資源タイプ
紀要論文
資源タイプ・ローカル
紀要論文
資源タイプ・NII
Departmental Bulletin Paper
資源タイプ・DCMI
text
資源タイプ・ローカル表示コード
03
所属
Ochanomizu University
Information Processing Center, Ochanomizu University
Pell Equation. I. Systematic classification of the solutions of the Pell equation
KJ00004830808.pdf
(1.19MB)
