Common terms of Leonardo and Jacobsthal numbers

In this paper, we investigate the common terms of the Leonardo {Len}n≥0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\{ Le_n\}_{n \ge 0}$$\end{document} and Jacobsthal {Jm}m≥0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\{ J_{m} \}_{m \ge 0}$$\end{document} 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 Len=Jm\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$Le_n=J_m$$\end{document}.