Generalization of a theorem of Adegbindin, Luca and Togbé

Let k≥2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k\ge 2$$\end{document}. A generalization of the well-known Pell sequence is the k-Pell sequence. For this sequence the first k terms are 0,…,0,1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$0,\ldots ,0,1$$\end{document} and each term afterwards is given by the linear recurrence Pn(k)=2Pn-1(k)+Pn-2(k)+⋯+Pn-k(k).\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{aligned} P_n^{(k)}=2P_{n-1}^{(k)}+P_{n-2}^{(k)}+\cdots +P_{n-k}^{(k)}. \end{aligned}$$\end{document}In this paper, our main objective is to find all k-Pell numbers which are sum of two repdigits. This generalizes a result of Adegbindin et al. (Bull Malays Math Sci Soc 43:1253–1271, 2020) regarding Pell numbers with the above property.