Finding the Fundamental Solutions of the Pell Equation $ x^{2}-dy^{2}=pm 1$ by determining the Right Neighbor of $F=(d,0,-1)$

Tekcan A., Karadeniz Gözeri G.

Libertas Mathematica (new series), cilt.38, ss.45-57, 2018 (Hakemli Dergi)

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 38
  • Basım Tarihi: 2018
  • Dergi Adı: Libertas Mathematica (new series)
  • Derginin Tarandığı İndeksler: MathSciNet
  • Sayfa Sayıları: ss.45-57
  • İstanbul Üniversitesi Adresli: Evet

Özet

In this work we determine the fundamental solutions of the Pell equation $%
x^{2}-dy^{2}=\pm 1$ by determining the right neighbors of indefinite forms $%
F=(d,0,-1)$ of discriminant $\Delta =4d$ for some specific values
of $d $.