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withdrawed due to a substantial error.

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This paper has been withdrawn by the author due to serious flaws in certain proofs. For instance, the method used to construct certain automorphic representations is flawed.

This contribution presents all possible solutions to the Diophantine equations $F_k=L_mL_n$ and $L_k=F_mF_n$. To be clear, Fibonacci numbers that are the product of two arbitrary Lucas numbers and Lucas numbers that are the product of two…

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This paper has been withdrawn by the author due to an error in the data-analysis.