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k-Fibonacci numbers which are Padovan or Perrin numbers

Author

Listed:
  • Salah Eddine Rihane

    (University Center of Mila
    The National Higher School of Mathematics, Sidi Abdallah)

  • Alain Togbé

    (Purdue University Northwest)

Abstract

For an integer $$k\ge 2$$ k ≥ 2 , let $$(F_n^{(k)})_n$$ ( F n ( k ) ) n be the k-generalized Fibonacci sequence which starts with $$0,\ldots ,0,1,1$$ 0 , … , 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 $$F^{(k)}_n = P_m$$ F n ( k ) = P m and $$F^{(k)}_n = E_m$$ F n ( k ) = E m in positive integers n, k, m with $$k \ge 2$$ k ≥ 2 .

Suggested Citation

  • Salah Eddine Rihane & Alain Togbé, 2023. "k-Fibonacci numbers which are Padovan or Perrin numbers," Indian Journal of Pure and Applied Mathematics, Springer, vol. 54(2), pages 568-582, June.
    • Handle: RePEc:spr:indpam:v:54:y:2023:i:2:d:10.1007_s13226-022-00276-z
    DOI: 10.1007/s13226-022-00276-z
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