Title of article :
Diophantine Equations Related with Linear Binary Recurrences
Author/Authors :
Kilic ، Emrah Department of Mathematics - TOBB University of Economics and Technology , Akkus ، Ilker Department of Mathematics - Faculty of Arts and Science - Kırıkkale University , Omur ، Nese Department of Mathematics - Faculty of Arts and Science - Kocaeli University
Abstract :
In this paper we find all solutions of four kinds of the Diophantine equations x² ± V_t xy − y² ± x = 0 and x² ± Vtxy − y² ± y = 0, for an odd number t, and, x² ± V_t xy + y² − x = 0 and x² ± Vtxy + y² − y = 0, for an even number t, where V_n is a generalized Lucas number. This paper continues and extends a previous work of Bahramian and Daghigh.
Keywords :
Linear recurrences , Generalized Fibonacci and Lucas sequences , Diophantine equations , Continued fractions
Journal title :
Iranian Journal of Mathematical Sciences and Informatics (IJMSI)
Journal title :
Iranian Journal of Mathematical Sciences and Informatics (IJMSI)
