Results 1 to 10 of about 10,646,047 (124)
On the Inverse of a Fibonacci Number Modulo a Fibonacci Number Being a Fibonacci Number
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 $\gcd(a, b) > 1$.
C. Sanna
openaire +3 more sources
Some equalities and binomial sums about the generalized Fibonacci number $u_n$
Notes on Number Theory and Discrete Mathematics, 2022 In this study, we take the generalized Fibonacci sequence \{u_{n}\} as u_{0}=0,u_{1}=1 and \ u_{n}=ru_{n-1}+u_{n-2} for n>1, where r is a non-zero integer.
Yücel Türker Ulutaş, Derya Toy
semanticscholar +1 more source
Hybrid Numbers with Fibonacci and Lucas Hybrid Number Coefficients
Universal Journal of Mathematics and Applications, 2023 In this paper, we introduce hybrid numbers with Fibonacci and Lucas hybrid number coefficients. We give the Binet formulas, generating functions, exponential generating functions for these numbers. Then we define an associate matrix for these numbers. In
E. Polatlı
semanticscholar +1 more source
On the greatest common divisor of n and the nth Fibonacci number, II [PDF]
Canadian mathematical bulletin, 2017 Let $\mathcal {A}$ be the set of all integers of the form $\gcd (n, F_n)$ , where n is a positive integer and $F_n$ denotes the nth Fibonacci number. Leonetti and Sanna proved that $\mathcal {A}$ has natural density equal to zero, and asked for a
A. Jha, C. Sanna
semanticscholar +1 more source
The density of numbersnhaving a prescribed G.C.D. with thenth Fibonacci number [PDF]
Indagationes mathematicae, 2017 For each positive integer $k$, let $\mathscr{A}_k$ be the set of all positive integers $n$ such that $\gcd(n, F_n) = k$, where $F_n$ denotes the $n$th Fibonacci number.
C. Sanna, Emanuele Tron
semanticscholar +1 more source
True Random Number Generator Based on Fibonacci-Galois Ring Oscillators for FPGA
Applied Sciences, 2021 Random numbers are widely employed in cryptography and security applications. If the generation process is weak, the whole chain of security can be compromised: these weaknesses could be exploited by an attacker to retrieve the information, breaking even
P. Nannipieri +6 more
semanticscholar +1 more source
On generalized Fibonacci numbers [PDF]
Applied Mathematical Sciences, 2015 We provide a formula for the $n^{th}$ term of the $k$-generalized Fibonacci-like number sequence using the $k$-generalized Fibonacci number or $k$-nacci number, and by utilizing the newly derived formula, we show that the limit of the ratio of successive terms of the sequence tends to a root of the equation $x + x^{-k} = 2$.
Bacani, Jerico B. +1 more
openaire +2 more sources
On the sum of a prime and a Fibonacci number [PDF]
, 2010 We show that the set of the numbers that are the sum of a prime and a Fibonacci number has positive lower asymptotic density.
K. E. Lee
semanticscholar +1 more source
Fibonacci number of the tadpole graph
Electronic Journal of Graph Theory and Applications, 2014 In 1982, Prodinger and Tichy defined the Fibonacci number of a graph G to be the number of independent sets of the graph G. They did so since the Fibonacci number of the path graph Pn is the Fibonacci number Fn+2 and the Fibonacci number of the cycle ...
J. DeMaio, J. Jacobson
semanticscholar +1 more source
On the golden number and Fibonacci type sequences
, 2020 The paper presents, among others, the golden number $\varphi$ as the limit of the quotient of neighboring terms of the Fibonacci and Fibonacci type sequence by means of a fixed point of a mapping of a certain interval with the help of Edelstein's theorem.
Eugeniusz Barcz
semanticscholar +1 more source