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), vol.38, pp.45-57, 2018 (Peer-Reviewed Journal)

  • Publication Type: Article / Article
  • Volume: 38
  • Publication Date: 2018
  • Journal Name: Libertas Mathematica (new series)
  • Journal Indexes: MathSciNet
  • Page Numbers: pp.45-57
  • Istanbul University Affiliated: Yes

Abstract

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 $.