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Diophantine Equations Involving Sums of Fibonacci and Jacobsthal Numbers
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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 $\{F_c\}_{c \geq 0}$ and $\{J_c}_{c\gec 0}$
are the sequences of Fibonacci and Jacobsthal numbers, respectively. An adaptation of Baker’s theorem for linear forms in logarithms and Dujella and Pethő’s reduction method confirms our main results.
Universiti Putra Malaysia
Title: Diophantine Equations Involving Sums of Fibonacci and Jacobsthal Numbers
Description:
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 $\{F_c\}_{c \geq 0}$ and $\{J_c}_{c\gec 0}$
are the sequences of Fibonacci and Jacobsthal numbers, respectively.
An adaptation of Baker’s theorem for linear forms in logarithms and Dujella and Pethő’s reduction method confirms our main results.
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