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, Ahmet; Karadeniz Gözeri, GÜL

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

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 $.