Braided Gibonacci Sequences on Residue Classes

Jürgen Spilker () and Luu Ba Thang ()
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Jürgen Spilker: University of Freiburg, Institute of Mathematics
Luu Ba Thang: Hanoi National University of Education, Department of Mathematics and Informatics

A chapter in Number Theory in Memory of Eduard Wirsing, 2023, pp 323-333 from Springer

Abstract: 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 $$F_{2n+1}-1$$ .

Keywords: Fibonacci sequence; Braided sequences (search for similar items in EconPapers)
Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-031-31617-3_22

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DOI: 10.1007/978-3-031-31617-3_22

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