Continued fractions expansion of √D and Pell equation x2 - Dy2 = 1

Abstract

Let D ≠ = 1 be a positive non-square integer. In the first section, we give some preliminaries from Pell equations and simple continued fraction expansion. In the second section, we give a formula for the continued fraction expansion of √D for some specific values of D and then we consider the integer solutions of Pell equations x2-Dy2 = 1 for these values of D including recurrence relations on the integer solutions of it.