Solutions of some diophantine equations in terms of horadam sequence

Abstract

Let a, b, and P be integers such that (a, b) 6= (0, 0). In this study, we give all solutions of the equations x2 − Pxy − y2 = ±(b2 − Pab − a2), x2 − (P2 + 4)y2 = ±4(b2 − Pab − a2), x2−(P2+4)y2 = ±4(b2−Pab−a2)2, x2−Pxy+y2 = b2−Pab+a2, x2−(P2−4)y2 = 4(b2−Pab+a2), and x2 − (P2 − 4)y2 = 4(b2 − Pab + a2)2 in terms of the second order recurrence sequences when |b2 − Pab ± a2| is odd prime. © 2019 A. Razmadze Mathematical Institute of Iv. Javakhishvili Tbilisi State University. All rights reserved.