Solving Pell's equation using suborbital graphs
FILOMAT, cilt.38, sa.19, ss.6863-6870, 2024 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 38 Sayı: 19
- Basım Tarihi: 2024
- Doi Numarası: 10.2298/fil2419863k
- Dergi Adı: FILOMAT
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
- Sayfa Sayıları: ss.6863-6870
- Karadeniz Teknik Üniversitesi Adresli: Evet
Özet
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.