Solving Pell's equation using suborbital graphs

被引：0
|
作者：
Koroglu, Tuncay [1 ]
机构：
[1] Karadeniz Tech Univ, Trabzon, Turkiye
来源：
FILOMAT | 2024年 / 38卷 / 19期
关键词：
Modular group action; Suborbital graph; Pell's equation; CONGRUENCE SUBGROUPS;
D O I：
10.2298/FIL2419863K
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We establish a connection between suborbital graphs and integer solutions of Pell's equation of the form x(2) - Ny(2) = 1, where N is a non-square positive integer. We derive new suborbital graphs generated by the action of some specific modular subgroups on extended rational numbers. By using these graphs, we obtain a new combinatorial notation for the integer solutions of Pell's equation and some results on the vertices of the graphs studied here.
引用
收藏
页码：6863 / 6870
页数：8
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