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On perfect powers that are sums of two Pell numbers

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Abstract

Let \(P_k\) denote the kth term of the Pell sequence. In this paper we find all solutions of the exponential Diophantine equation \(P_n+P_m = y^s\) in positive integer variables (m, n, y, s) under the assumption \(n \equiv m \pmod 2\).

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Acknowledgements

We thank the referees for useful comments to improve the quality of this paper. SER was partially supported by DGRSDT. AT was supported in part by Purdue University Northwest.

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Authors and Affiliations

  1. Computer Science Department, Petree College of Art and Science (PCAS), Oklahoma City University, 2501 N Blackwelder, Oklahoma City, OK, 73106-1493, USA

    Hyacinthe Aboudja

  2. Laboratoire d’Algèbre et Théorie des Nombres, Faculté de Mathématiques, Université des Sciences et de la Technologie Houari-Boumediène (USTHB), BP 32, 16111, Bab-Ezzouar Alger, Algeria

    Mohand Hernane

  3. Laboratory of Algebra and Number Theory, Faculty of Mathematics, University of Sciences and Technology Houari Boumediene, BP 32, 16111, Algiers, Algeria

    Salah Eddine Rihane

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

    Alain Togbé

Authors
  1. Hyacinthe Aboudja
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  2. Mohand Hernane
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  3. Salah Eddine Rihane
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  4. Alain Togbé
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Correspondence to Alain Togbé.

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Aboudja, H., Hernane, M., Rihane, S.E. et al. On perfect powers that are sums of two Pell numbers. Period Math Hung 82, 11–15 (2021). https://doi.org/10.1007/s10998-020-00342-1

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  • DOI: https://doi.org/10.1007/s10998-020-00342-1

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