Randomized trial identifies solutions to Diophantine equation involving Fibonacci and Jacobsthal numbers, suggesting unique factorization.
In the present paper, we identify all Jacobsthal numbers that may be expressed as a product of three Fibonacci numbers. More precisely, our main result shows that the only solution to the Diophantine equationFkFlFm = Jnfor 2 < k < l < m is expressed as (k,l,m,n) = (5,7,8,12). The proof relies on techniquesinvolving linear forms in logarithms.
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Kim et al. (2026) studied this question.
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