The Polynomial Solutions of Quadratic Diophantine Equation X2−ptY2+2KtX+2ptLtY = 0 - Hasan Sankari; Ahmad Abdo (Journal of Mathematics, 2021)
In this study, we consider the number of polynomial solutions of the Pell equation x2−pty2=2 is formulated for a nonsquare polynomial pt using the polynomial solutions of the Pell equation x2−pty2=1. Moreover, a recurrence relation on the polynomial solutions of the Pell equation x2−pty2=2. Then, we consider the number of polynomial solutions of Diophantine equation E: X2−ptY2+2KtX+2ptLtY=0. We also obtain some formulas and recurrence relations on the polynomial solution Xn,Yn of E.