On the solutions of 2x + 2y = z2 in the Fibonacci and Lucas numbers

Authors

  • Hayder R. Hashim Faculty of Computer Science and Mathematics, University of Kufa, P.O. Box 21, 54001 Al Najaf, Iraq.

Keywords:

Diophantine equations, exponential Diophantine equations, Fibonacci sequence, Lucas sequence

Abstract

Consider the Diophantine equation 2x + 2y = z2, where x, y and z are nonnegative integers. As thisequation has infinitely many solutions, in this paper we study its solutions in case where the unknowns represent Fibonacci and/or Lucas numbers. In other words, we completely resolve the equation in case of (x, y, z) ∈ {(Fi, Fj , Fk),(Fi, Fj ,Lk),(Li,Lj ,Lk),(Li,Lj , Fk),(Fi,Lj ,Lk),(Fi,Lj , Fk)} with i, j, k ≥ 1 and Fn and Ln denote the general terms of Fibonacci and Lucas numbers, respectively.

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Published

2023-06-30

Issue

Vol. 19 No. 1 (2023): Journal of Prime Research in Mathematics

Section

Regular

How to Cite

On the solutions of 2x + 2y = z2 in the Fibonacci and Lucas numbers. (2023). Journal of Prime Research in Mathematics, 19(1), 27 – 33. https://jprm.sms.edu.pk/index.php/jprm/article/view/205