Results 31 to 40 of about 2,057 (213)
On the bounds for the spectral norms of geometric circulant matrices
Journal of Inequalities and Applications, 2016 In this paper, we define a geometric circulant matrix whose entries are the generalized Fibonacci numbers and hyperharmonic Fibonacci numbers. Then we give upper and lower bounds for the spectral norms of these matrices.
Can Kızılateş, Naim Tuglu
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Perfect numbers and Fibonacci primes (I) [PDF]
International Journal of Number Theory, 2014 In this paper, we introduce the concept of F-perfect number, which is a positive integer n such that ∑d|n,d<n d2 = 3n. We prove that all the F-perfect numbers are of the form n = F2k-1 F2k+1, where both F2k-1 and F2k+1 are Fibonacci primes. Moreover, we obtain other interesting results and raise a new conjecture on perfect numbers.
Tianxin Cai, Deyi Chen, Yong Zhang
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Three new classes of binomial Fibonacci sums [PDF]
Transactions on CombinatoricsIn this paper, we introduce three new classes of binomial sums involving Fibonacci (Lucas) numbers and weighted binomial coefficients. One particular result is linked to a problem proposal recently published in the journal The Fibonacci Quarterly.
Robert Frontczak
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Fibonacci Numbers and Identities
The Fibonacci Quarterly, 2013 By investigating a recurrence relation about functions, we first give alternative proofs of various identities on Fibonacci numbers and Lucas numbers, and then, make certain well known identities visible via certain trivalent graph associated to the recurrence relation.
Lang, Cheng Lien, Lang, Mong Lung
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The limit of reciprocal sum of some subsequential Fibonacci numbers
AIMS Mathematics, 2021 This paper deals with the sum of reciprocal Fibonacci numbers. Let $ f_0 = 0 $, $ f_1 = 1 $ and $ f_{n+1} = f_n+f_{n-1} $ for any $ n\in\mathbb{N} $. In this paper, we prove new estimates on $ \sum\limits^\infty_{k = n}\frac{1}{f_{mk-\ell}} $, where ...
Ho-Hyeong Lee, Jong-Do Park
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On a generalization of the Pell sequence [PDF]
Mathematica Bohemica, 2021 The Pell sequence $(P_n)_{n=0}^{\infty}$ is the second order linear recurrence defined by $P_n=2P_{n-1}+P_{n-2}$ with initial conditions $P_0=0$ and $P_1=1$.
Jhon J. Bravo +2 more
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Fibonacci factoriangular numbers
Indagationes Mathematicae, 2017 Abstract Let ( F m ) m ≥ 0 be the Fibonacci sequence given by F 0 = 0 , F 1 = 1 and F m + 2 = F m + 1 + F m , for all m ≥ 0 . In Castillo (2015), it is conjectured that 2 , 5 and 34 are the only Fibonacci numbers of the form n ! + n
Florian Luca +2 more
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On Mixed Concatenations of Fibonacci and Lucas Numbers Which are Fibonacci Numbers
, 2022 Let $(F_n)_{n\geq 0}$ and $(L_n)_{n\geq 0}$ be the Fibonacci and Lucas sequences, respectively. In this paper we determine all Fibonacci numbers which are mixed concatenations of a Fibonacci and a Lucas numbers. By mixed concatenations of $ a $ and $ b $, we mean the both concatenations $\overline{ab}$ and $\overline{ba}$ together, where $ a $ and $ b $
Altassan, Alaa, Alan, Murat
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Divisibility of Fibonomial coefficients in terms of their digital representations and applications
AIMS Mathematics, 2022 We give a characterization for the integers $ n \geq 1 $ such that the Fibonomial coefficient $ {pn \choose n}_F $ is divisible by $ p $ for any prime $ p \neq 2, 5 $.
Phakhinkon Napp Phunphayap +1 more
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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 ...
Ma, Yuankui, Zhang, Wenpeng
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