Solving Pell's equation using suborbital graphs

KÖROĞLU T.

FILOMAT, cilt.38, sa.19, ss.6863-6870, 2024 (SCI-Expanded) identifier identifier

  • 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.