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Generalization of a theorem of Adegbindin, Luca and Togbé

Authors
  • Meguedmi, Djohra1
  • Rihane, Salah Eddine2
  • Togbé, Alain3
  • 1 Ecole Nationale Supérieure de Technologie, Cité Diplomatique (Ex Centre Biomédical), Dergana, Bordj El Kiffan, Alger, 16000, Algérie , Alger (Algeria)
  • 2 University Center of Mila, Mila, Algeria , Mila (Algeria)
  • 3 Purdue University Northwest, 1401 S, U.S. 421, Westville, IN, 46391, USA , Westville (United States)
Type
Published Article
Journal
Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas
Publisher
Springer International Publishing
Publication Date
Nov 05, 2021
Volume
116
Issue
1
Identifiers
DOI: 10.1007/s13398-021-01177-2
Source
Springer Nature
Keywords
Disciplines
  • Original Paper
License
Yellow

Abstract

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.

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