The Diophantine equation $\displaystyle a \left(\frac{b^k - 1}{b - 1}\right) = \mathcal{U}_n - \mathcal{U}_m$ P. Tiebekabe (  pagdame.tiebekabe@ucad.edu.sn ) Université de Kara https://orcid.org/0000-0002-1526-0062 I. Diouf UCAD A. Tall UCAD K. R. Kakanou UCAD Research Article Keywords: Linear forms in logarithm, Diophantine equations, Linear recurrent sequences, Lucas number, Pell number, Baker's theory, Reduction procedure Posted Date: June 9th, 2023 DOI: https://doi.org/10.21203/rs.3.rs-3040689/v1 License:   This work is licensed under a Creative Commons Attribution 4.0 International License. Read Full License