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k-Fibonacci numbers which are Padovan or Perrin numbers

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Abstract

For an integer \(k\ge 2\), let \((F_n^{(k)})_n\) be the k-generalized Fibonacci sequence which starts with \(0,\ldots ,0,1,1\) (k terms) and each term afterwards is the sum of the k preceding terms. In this paper, we find all the k-generalized Fibonacci numbers which are Padovan or Perrin numbers i.e., we solve the Diophantine equation \(F^{(k)}_n = P_m\) and \(F^{(k)}_n = E_m\) in positive integers n, k, m with \(k \ge 2\).

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Authors and Affiliations

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

    Salah Eddine Rihane

  2. The National Higher School of Mathematics, Sidi Abdallah, Algiers, 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

Authors
  1. Salah Eddine Rihane
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  2. Alain Togbé
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Correspondence to Alain Togbé.

Additional information

Communicated by B. Sury.

AT was supported in part by Purdue University Northwest.

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Rihane, S.E., Togbé, A. k-Fibonacci numbers which are Padovan or Perrin numbers. Indian J Pure Appl Math 54, 568–582 (2023). https://doi.org/10.1007/s13226-022-00276-z

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  • DOI: https://doi.org/10.1007/s13226-022-00276-z

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