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Common terms of Leonardo and Jacobsthal numbers

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Abstract

In this paper, we investigate the common terms of the Leonardo \(\{ Le_n\}_{n \ge 0}\) and Jacobsthal \(\{ J_{m} \}_{m \ge 0}\) sequences. To accomplish this, we use Baker’s theory of linear forms in logarithms of algebraic numbers along with a variation of the Baker-Davenport reduction method to solve the Diophantine equation \(Le_n=J_m\).

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Acknowledgements

The authors express their sincere gratitude to the referee for their careful reading of the manuscript and many useful comments that improved the quality of the paper.

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Authors and Affiliations

  1. Faculty of Computer Sciences, USTHB, BP 32, El Alia, 16111, Bab Azzouar, Algiers, Algeria

    Hayat Bensella

  2. Faculty of Mathematics, LATN Laboratory, USTHB, BP 32, El Alia, 16111, Bab Azzouar, Algiers, Algeria

    Djilali Behloul

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  1. Hayat Bensella
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  2. Djilali Behloul
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Correspondence to Hayat Bensella.

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Bensella, H., Behloul, D. Common terms of Leonardo and Jacobsthal numbers. Rend. Circ. Mat. Palermo, II. Ser 73, 259–265 (2024). https://doi.org/10.1007/s12215-023-00920-5

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