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

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 valuesof $d $.