Malaysian Journal of Mathematical Sciences, June 2026, Vol. 20, No. 2
Diophantine Equations Involving Sums of Fibonacci and Jacobsthal Numbers
Tarek, S., Anwar, M., Elsonbaty, A., Gaber, A.
Corresponding Email: starek98@sci.asu.edu.eg
Received date: 8 March 2025
Accepted date: 30 September 2025
Abstract:
This study identifies all Fibonacci numbers that can be expressed as the sum of two Jacobsthal numbers and all Jacobsthal numbers that can be expressed as the sum of two Fibonacci numbers. More precisely, we identify every non-negative integer solution \((a,\ b,\ c)\) of the Diophantine equations \(F_a +F_b =J_c\) and \(J_a +J_b =F_c\), where {\(F_c\)}c≥0 and {\(J_c\)}c≥0 are the sequences of Fibonacci and Jacobsthal numbers, respectively. An adaptation of Baker's theorem for linear forms in logarithms and Dujella and Pethö's reduction method confirms our main results.
Keywords: Fibonacci sequence; Jacobsthal sequence; linear forms in logarithms; reduction method.
