Positive Integer Solutions of Some Pell Equations via Generalized Bi-Periodic Fibonacci and Generalized Bi-Periodic Lucas Sequences

S. Sriram, P. Veeramallan

Abstract: Let C be a non-perfect square positive-integer and C=m^2?1,m^2?2,m^2?m. The basic solution of the Pell equation is found in the present articlex^2-Cy^2=?1by using Continued fraction expansion of ?C. Also, in terms of Generalized Bi-Periodic Fibonacci and Lucas sequences, we obtain all positive-integer solutions of the Pell equation x^2-Cy^2=?1.

Keywords: Continued fraction, Pell equations, Generalized Bi-Periodic Fibonacci and Lucas sequences