On a Diophantine Equation with Jacobsthal and Fibonacci Numbers

Key Points

• This research aims to identify Jacobsthal numbers that can be expressed as the product of three Fibonacci numbers.
• Identified solutions to the Diophantine equation FkFlFm = Jn for k,l,m,n values.
• Analyzed the equation with k<l<m and techniques involving linear forms in logarithms.
• The only solution found is (k,l,m,n) = (5,7,8,12).
• Demonstrated that no other combinations fit the criteria for expressing Jacobsthal numbers.