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Braided Gibonacci Sequences on Residue Classes

In: Number Theory in Memory of Eduard Wirsing

Author

Listed:
  • Jürgen Spilker

    (University of Freiburg, Institute of Mathematics)

  • Luu Ba Thang

    (Hanoi National University of Education, Department of Mathematics and Informatics)

Abstract

Let ( F n ) n ≥ 0 $$(F_n)_{n\geq 0}$$ be the Fibonacci sequence and ( L n ) n ≥ 0 $$(L_n)_{n\geq 0}$$ be the Lucas sequence and set h n : = F n $$h_n:=F_n$$ if n is even and h n : = L n $$h_n:=L_n$$ if n is odd. We study this braided sequence ( h n ) n ≥ 0 $$(h_n)_{n\geq 0}$$ , the restriction on a residue class, and find identities such as the greatest common divisor of F 2 n $$F_{2n}$$ and F 2 n + 1 − 1 $$F_{2n+1}-1$$ .

Suggested Citation

  • Jürgen Spilker & Luu Ba Thang, 2023. "Braided Gibonacci Sequences on Residue Classes," Springer Books, in: Helmut Maier & Jörn Steuding & Rasa Steuding (ed.), Number Theory in Memory of Eduard Wirsing, pages 323-333, Springer.
    • Handle: RePEc:spr:sprchp:978-3-031-31617-3_22
    DOI: 10.1007/978-3-031-31617-3_22
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