Results 11 to 20 of about 50 (49)
On the Generalized Order-$k$ Fibonacci and Lucas Numbers
Rocky Mountain Journal of Mathematics, 2006 In this paper we consider the generalized order-k Fibonacci and Lucas numbers. We give the generalized Binet formula, combinatorial representation and some relations involving the generalized order-k Fibonacci and Lucas numbers.
Kiliç, Emrah, Taşci, Dursun
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An identity for the Fibonacci and Lucas numbers [PDF]
Glasgow Mathematical Journal, 1993 In this paper we prove an identity between sums of reciprocals of Fibonacci and Lucas numbers. The Fibonacci numbers are defined for all n ≥ 0 by the recurrence relation Fn + 1 = Fn + Fn-1 for n ≥ 1, where F0 = 0 and F1 = 0. The Lucas numbers Ln are defined for all n ≥ 0 by the same recurrence relation, where L0 = 2 and L1 = 1 We prove the following ...
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On $k$-Fibonacci balancing and $k$-Fibonacci Lucas-balancing numbers
Carpathian Mathematical Publications, 2021 The balancing number $n$ and the balancer $r$ are solution of the Diophantine equation $$1+2+\cdots+(n-1) = (n+1)+(n+2)+\cdots+(n+r). $$ It is well known that if $n$ is balancing number, then $8n^2 + 1$ is a perfect square and its positive square root is called a Lucas-balancing number.
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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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Some properties of Fibonacci numbers, Fibonacci octonions, and generalized Fibonacci-Lucas octonions [PDF]
Advances in Difference Equations, 2015 In this paper we determine some properties of Fibonacci octonions. Also, we introduce the generalized Fibonacci-Lucas octonions and we investigate some properties of these elements.
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Determinantal Identities of Fibonacci, Fibonacci Like and Lucas Numbers
Turkish Journal of Analysis and Number Theory, 2014 Determinants have played a significant part in various areas in mathematics. For instance, they are quite useful in the analysis and solution of system of linear equations. There are different perspectives on the study of determinant. In this paper we present some determinant identities of Fibonacci and Lucas numbers.
Sanjay Harne +2 more
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The imperfect Fibonacci and Lucas numbers
Irish Mathematical Society Bulletin, 2009 A perfect number is any positive integer that is equal to the sum of its proper divisors. Several years ago, F. Luca showed that the Fibonacci and Lucas numbers contain no perfect numbers. In this paper, we alter the argument given by Luca for the nonexistence of both odd perfect Fi- bonacci and Lucas numbers, by making use of an 1888 result of C ...
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A Study on Dual Hyperbolic Fibonacci and Lucas Numbers
Analele Universitatii "Ovidius" Constanta - Seria Matematica, 2019 Abstract In this study, the dual-hyperbolic Fibonacci and dual-hyperbolic Lucas numbers are introduced. Then, the fundamental identities are proven for these numbers. Additionally, we give the identities regarding negadual-hyperbolic Fibonacci and negadual-hyperbolic Lucas numbers.
Sakarya Üniversitesi/Eğitim Fakültesi/Matematik Ve Fen Bilimleri Eğitimi Bölümü +7 more
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On the products of \(k\)-Fibonacci numbers and \(k\)-Lucas numbers
Int. J. Math. Math. Sci., 2014 Summary: In this paper, we investigate some products of \(k\)-Fibonacci and \(k\)-Lucas numbers. We also present some generalized identities on the products of \(k\)-Fibonacci and \(k\)-Lucas numbers to establish connection formulas between them with the help of Binet's formula.
Bijendra Singh +2 more
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