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Generalization of a theorem of Adegbindin, Luca and Togbé

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Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas Aims and scope Submit manuscript

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Abstract

Let \(k\ge 2\). A generalization of the well-known Pell sequence is the k-Pell sequence. For this sequence the first k terms are \(0,\ldots ,0,1\) and each term afterwards is given by the linear recurrence

$$\begin{aligned} P_n^{(k)}=2P_{n-1}^{(k)}+P_{n-2}^{(k)}+\cdots +P_{n-k}^{(k)}. \end{aligned}$$

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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Authors and Affiliations

  1. Ecole Nationale Supérieure de Technologie, Cité Diplomatique (Ex Centre Biomédical), Dergana, Bordj El Kiffan, 16000, Alger, Algérie

    Djohra Meguedmi

  2. Department of Mathematics, Institute of Science and Technology, University Center of Mila, Mila, Algeria

    Salah Eddine Rihane

  3. Department of Mathematics, Statistics, and Computer Science, Purdue University Northwest, 1401 S, U.S. 421, Westville, IN, 46391, USA

    Alain Togbé

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  1. Djohra Meguedmi
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  2. Salah Eddine Rihane
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  3. Alain Togbé
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Correspondence to Alain Togbé.

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Meguedmi, D., Rihane, S.E. & Togbé, A. Generalization of a theorem of Adegbindin, Luca and Togbé. RACSAM 116, 36 (2022). https://doi.org/10.1007/s13398-021-01177-2

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  • DOI: https://doi.org/10.1007/s13398-021-01177-2

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