Results 1 to 10 of about 50 (49)
Some Applications of Fibonacci and Lucas Numbers [PDF]
, 2021 In this paper, we provide new applications of Fibonacci and Lucas numbers. In some circumstances, we find algebraic structures on some sets defined with these numbers, we generalize Fibonacci and Lucas numbers by using an arbitrary binary relation over the real fields instead of addition of the real numbers and we give properties of the new obtained ...
Cristina Flaut +2 more
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Fibonacci or Lucas numbers that are products of two Lucas numbers or two Fibonacci numbers
, 2023 This contribution presents all possible solutions to the Diophantine equations $F_k=L_mL_n$ and $L_k=F_mF_n$. To be clear, Fibonacci numbers that are the product of two arbitrary Lucas numbers and Lucas numbers that are the product of two arbitrary Fibonacci numbers are determined herein.
Daşdemir, Ahmet, Emin, Ahmet
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On the Intersections of Fibonacci, Pell, and Lucas Numbers [PDF]
Integers, 2011 AbstractWe describe how to compute the intersection of two Lucas sequences of the ...
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Fibonacci numbers and Lucas numbers in graphs
Discrete Applied Mathematics, 2009 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Mariusz Startek +2 more
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Alternating sums of the powers of Fibonacci and Lucas numbers [PDF]
Miskolc Mathematical Notes, 2011 We shall consider alternating Melham's sums for Fibonacci and Lucas numbers of the form Sigma(n)(k=1) (-1)(k) F-2k+delta(2m+epsilon) and Sigma(n)(k=1) (-1)(k) L-2k+delta(2m+epsilon), where epsilon, delta is an element of {0, 1}.
Ömür, Neşe +2 more
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Identities for Fibonacci and Lucas numbers
Notes on Number Theory and Discrete Mathematics, 2023 In this paper several new identities are given for the Fibonacci and Lucas numbers. This is accomplished by by solving a class of non-homogeneous, linear recurrence relations.
George Grossman +2 more
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A fast recurrence for Fibonacci and Lucas numbers
CoRR, 2021 We derive the double recurrence $e_n = \frac{1}{2}(a_{n-1}+5b_{n-1}); f_{n} = \frac{1}{2}(a_{n-1}+b_{n-1})$ with $e_0=2;f_0=0$ for the Fibonacci numbers, leading to an extremely simple and fast implementation. Though the recurrence is probably not new, we have not been able to find a reference for it.
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ON THE SEQUENCES RELATED TO FIBONACCI AND LUCAS NUMBERS [PDF]
Journal of the Korean Mathematical Society, 2005 The sequences \(\{U_n\}_{n\geq 0}\) and \(\{V_n\}_{n\geq 0}\) are introduced by recurrence relations: \[ \begin{aligned} U_n &= (q- 2)(U_{n-2}- U_{n-4},\;n\geq 4,\\ V_n &= (q-2) V_{n-2}- V_{n-4},\;n\geq 4\end{aligned} \] with initial conditions \(U_0= 0\), \(U_1= 1\), \(U_2= 1\), \(U_4= q- 1\), \(V_0= 2\), \(V_1= 1\), \(V_2= q-1\), where \(q\geq 5\) is
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A new approach to Fibonacci Tessarines with Fibonacci and Lucas number components
Adıyaman University Journal of Science, 2021 In this paper, by using identities related to the tessarines, Fibonacci numbers and Lucas numbers we define Fibonacci tessarines and Lucas tessarines. We obtain Binet formulae, D’ocagnes identity and Cassini identity for these tessarines. We also give the identities of Fibonacci negatessarines and Lucas negatessarines and define new vector which are ...
BABADAĞ, Faik, USLU, Merve
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Gaussian Fibonacci And Gaussian Lucas p-Numbers.
Ars Comb., 2017 In this paper we define and study the Gaussian Fibonacci and Gaussian Lucas p-numbers. We give generating functions, Binet formulas, explicit formulas, matrix representations and sums of Gaussian Fibonacci p-numbers by matrix methods . For p = 1 these Gaussian Fibonacci and Gaussian Lucas p-numbers reduce to the Gaussian Fibonacci and the Gaussian ...
Aşçı, Mustafa, Gürel, Eşref
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