Results 11 to 20 of about 31,264 (197)

Bi-Periodic (p,q)-Fibonacci and Bi-Periodic (p,q)-Lucas Sequences

Sakarya Üniversitesi Fen Bilimleri Enstitüsü Dergisi, 2023
In this paper, we define bi-periodic (p,q)-Fibonacci and bi-periodic (p,q)-Lucas sequences, which generalize Fibonacci type, Lucas type, bi-periodic Fibonacci type and bi-periodic Lucas type sequences, using recurrence relations of (p,q)-Fibonacci and (p,
Yasemin Taşyurdu, Naime Şeyda Türkoğlu   +1 more
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There are no multiply-perfect Fibonacci numbers [PDF]

, 2011
Here, we show that no Fibonacci number (larger than 1) divides the sum of its ...
Alain Togbé, Bugeaud Y., Florian Luca, Kevin A. Broughan, Luca F., Marcos J. González, Robbins N., Rosser J. B., Ryan H. Lewis, V. Janitzio Mejía Huguet   +9 more
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Some fundamental Fibonacci number congruences [PDF]

Notes on Number Theory and Discrete Mathematics
This paper investigates a number of congruence properties related to the coefficients of a generalized Fibonacci polynomial. This polynomial was defined to produce properties comparable with those of the standard polynomials of some special functions ...
Anthony G. Shannon, Tian-Xiao He, Peter J.-S. Shiue, Shen C. Huang   +3 more
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Diophantine equations with Lucas and Fibonacci number coefficients [PDF]

Notes on Number Theory and Discrete Mathematics
Fibonacci and Lucas numbers are special number sequences that have been the subject of many studies throughout history due to the relations they provide.
Cemil Karaçam, Alper Vural, Bilal Aytepe, Ferhat Yıldız   +3 more
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Some properties of the generalized (p,q)- Fibonacci-Like number

MATEC Web of Conferences, 2018
For the real world problems, we use some knowledge for explain or solving them. For example, some mathematicians study the basic concept of the generalized Fibonacci sequence and Lucas sequence which are the (p,q) – Fibonacci sequence and the (p,q ...
Suvarnamani Alongkot
doaj   +1 more source

Power Fibonacci sequences in quadratic integer modulo m [PDF]

Notes on Number Theory and Discrete Mathematics
The power Fibonacci sequence in ℤₘ[√δ] is defined as a Fibonacci sequence Fₙ=Fₙ₋₁+Fₙ₋₂ where F₀=1 and F₁=a, such that a∈ℤₘ[√δ] and Fₙ≡aⁿ(mod m), for all n∈ℕ∪{0}. In this paper, we investigated the existence of power Fibonacci sequences in ℤₘ[√δ], and the
Paul Ryan A. Longhas, Cyryn Jade L. Prendol, Jenelyn F. Bantilan, Larra L. De Leon   +3 more
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Tunable multichannel Fibonacci one-dimensional terahertz photonic crystal filter

Scientific Reports, 2023
This paper proposes a multichannel terahertz optical filter based on a one-dimensional photonic crystal with a third-order Fibonacci structure, including a bulk Dirac semimetal.
V. Sepahvandi, B. Rezaei, A. H. Aly
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The Fibonacci numbers of certain subgraphs of circulant graphs

AKCE International Journal of Graphs and Combinatorics, 2015
The Fibonacci number ℱ(G) of a graph G with vertex set V(G), is the total number of independent vertex sets S⊂V(G); recall that a set S⊂V(G) is said to be independent whenever for every two different vertices u,v∈S there is no edge between them.
Loiret Alejandría Dosal-Trujillo, Hortensia Galeana-Sánchez   +1 more
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New Properties and Identities for Fibonacci Finite Operator Quaternions

Mathematics, 2022
In this paper, with the help of the finite operators and Fibonacci numbers, we define a new family of quaternions whose components are the Fibonacci finite operator numbers. We also provide some properties of these types of quaternions.
Nazlıhan Terzioğlu, Can Kızılateş, Wei-Shih Du   +2 more
doaj   +1 more source

Physical Phenomenology of Phyllotaxis [PDF]

, 2011
We propose an evolutionary mechanism of phyllotaxis, regular arrangement of leaves on a plant stem. It is shown that the phyllotactic pattern with the Fibonacci sequence has a selective advantage, for it involves the least number of phyllotactic ...
Adler, Adler, Bryntsev, Coxeter, Coxeter, Douady, Fujita, Fujita, Graham, Hellwig, Jean, Kuhlemeier, Larson, Levitov, Marzec, Richards, Ridley, Rivier, Rothen, Rothen, Schwendener, Snow, Takuya Okabe, Thompson, Thornley, van Iterson, Zagórska-Marek   +26 more
core   +1 more source