Diophantine Equations Involving Sums of Fibonacci and Jacobsthal Numbers

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 Fa + Fb = Jcand Ja + Jb = Fc, where {Fc}c >= 0 and {Jc}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 Peth & odblac;'s reduction method confirms our main results.