SOLUTIONS OF THE PELL EQUATION x2 - (a2+2a) y2 = N VIA GENERALIZED FIBONACCI AND LUCAS NUMBERS

In this study, we find continued fraction expansion of Aid when d = a(2) + 2a where a is positive integer. We consider the integer solutions of the Pell equation x(2) - (a(2) + 2a) y(2) = N when N is an element of {+/-1, +/-4}. We formulate the n-th solution (x(n), y(n)) by using the continued fraction expansion. We also formulate the n-th solution (x(n), y(n)) via the generalized Fibonacci and Lucas sequences.