Results 1 to 10 of about 4,031 (226)
On the Inverse of a Fibonacci Number Modulo a Fibonacci Number Being a Fibonacci Number [PDF]
Mediterranean Journal of Mathematics, 2023 Let $(F_n)_{n \geq 1}$ be the sequence of Fibonacci numbers. For all integers $a$ and $b \geq 1$ with $\gcd(a, b) = 1$, let $[a^{-1} \!\bmod b]$ be the multiplicative inverse of $a$ modulo $b$, which we pick in the usual set of representatives $\{0, 1, \dots, b-1\}$. Put also $[a^{-1} \!\bmod b] := \infty$ when $\gcd(a, b) > 1$.
Carlo Sanna
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Some Identities Involving Fibonacci Polynomials and Fibonacci Numbers [PDF]
Mathematics, 2018 The aim of this paper is to research the structural properties of the Fibonacci polynomials and Fibonacci numbers and obtain some identities. To achieve this purpose, we first introduce a new second-order nonlinear recursive sequence. Then, we obtain our main results by using this new sequence, the properties of the power series, and the combinatorial ...
Wenpeng Zhang
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Notes on generalized and extended Leonardo numbers [PDF]
Notes on Number Theory and Discrete Mathematics, 2023 This paper both extends and generalizes recently published properties which have been developed by many authors for elements of the Leonardo sequence in the context of second-order recursive sequences.
Anthony G. Shannon +2 more
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An inequality for Fibonacci numbers
Mathematica Bohemica, 2022 Summary: We extend an inequality for Fibonacci numbers published by \textit{P. G. Popescu} and \textit{J. L. Díaz-Barrero} in [JIPAM, J. Inequal. Pure Appl. Math. 7, No. 2, Paper No. 41, 5 p. (2006; Zbl 1132.26011)].
Horst Alzer, Florian Luca
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Statistics on restricted Fibonacci words [PDF]
Transactions on Combinatorics, 2021 We study two foremost Mahonian statistics, the major index and the inversion number for a class of binary words called restricted Fibonacci words. The language of restricted Fibonacci words satisfies recurrences which allow for the calculation of the ...
Omer Egecloglu
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On Fibonacci functions with Fibonacci numbers [PDF]
Advances in Difference Equations, 2012 Abstract In this paper we consider Fibonacci functions on the real numbers R, i.e., functions f : R → R such that for all x ∈ R ,
Han, Jeong, Kim, Hee, Neggers, Joseph
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Novel Fibonacci and non-Fibonacci structure in the sunflower: results of a citizen science experiment [PDF]
Royal Society Open Science, 2016 This citizen science study evaluates the occurrence of Fibonacci structure in the spirals of sunflower (Helianthus annuus) seedheads. This phenomenon has competing biomathematical explanations, and our core premise is that observation of both Fibonacci ...
Jonathan Swinton, Erinma Ochu,
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Altered Numbers of Fibonacci Number Squared
Journal of New Theory, 2023 We investigate two types of altered Fibonacci numbers obtained by adding or subtracting a specific value $\{a\}$ from the square of the $n^{th}$ Fibonacci numbers $G^{(2)}_{F(n)}(a)$ and $H^{(2)}_{F(n)}(a)$.
Emre Kankal, Fikri Köken
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A Class of Fibonacci Matrices, Graphs, and Games
Mathematics, 2022 In this paper, we define a class of Fibonacci graphs as graphs whose adjacency matrices are obtained by alternating binary Fibonacci words. We show that Fibonacci graphs are close in size to Turán graphs and that their size-stability tradeoff defined as ...
Valentin E. Brimkov, Reneta P. Barneva
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Odd Fibonacci Stolarsky-3 Mean Labeling of Some Special Graphs
Ratio Mathematica, 2022 Let G be a graph with p vertices and q edges and an injective function where each is a odd Fibonacci number and the induced edge labeling are defined by and all these edge labeling are distinct is called Odd Fibonacci Stolarsky-3 Mean Labeling.
M Sree Vidya, S.S Sandhya
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