Results 1 to 10 of about 92,262 (258)
On the properties of Lucas numbers with binomial coefficients
Applied Mathematics Letters, 2010 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Necati Taskara +2 more
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Sums of Pell/Lucas Polynomials and Fibonacci/Lucas Numbers
Mathematics, 2022 Seven infinite series involving two free variables and central binomial coefficients (in denominators) are explicitly evaluated in closed form. Several identities regarding Pell/Lucas polynomials and Fibonacci/Lucas numbers are presented as consequences.
Dongwei Guo +2 more
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ALTERED NUMBERS OF LUCAS NUMBER SQUARED
Journal of Scientific Reports-A, 2023 We investigate two types altered Lucas numbers denoted and defined by adding or subtracting a value from the square of the Lucas numbers. We achieve these numbers form as the consecutive products of the Fibonacci numbers. Therefore, consecutive sum-subtraction relations of altered Lucas numbers and their Binet-like formulas are given by using ...
Fikri KÖKEN, Emre KANKAL
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Lucas factoriangular numbers [PDF]
Mathematica Bohemica, 2018 A positive integer is a factoriangular number if it is of the form \(n!+n(n+1)/2\) for \(n\ge 0\), see [\textit{R. C. Castillo}, Asia Pac. J. Multidiscipl. Res. 3, No. 4, 5--11 (2015; \url{http://www.apjmr.com/wp-content/uploads/2015/10/APJMR-2015-3.4.1.02.pdf})]. \textit{C. A. Gómez Ruiz} and \textit{F. Luca} [Indag. Math., New Ser. 28, No.
Bir Kafle, Florian Luca, Alain Togbé
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On square Tribonacci Lucas numbers
Hacettepe Journal of Mathematics and Statistics, 2021 The Tribonacci-Lucas sequence {Sn}{Sn} is defined by the recurrence relation Sn+3=Sn+2+Sn+1+SnSn+3=Sn+2+Sn+1+Sn with S0=3, S1=1, S2=3.S0=3, S1=1, S2=3. In this note, we show that 11 is the only perfect square in Tribonacci-Lucas sequence for n≢1(mod32)n≢1(mod32) and n≢17(mod96).n≢17(mod96).
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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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Square-free Lucas d-pseudoprimes and Carmichael-Lucas numbers [PDF]
Czechoslovak Mathematical Journal, 2007 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Carlip, W., Somer, L.
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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 Bicomplex Jacobsthal-Lucas Numbers
Journal of Mathematical Sciences and Modelling, 2020 In this study we introduced a sequence of bicomplex numbers whose coefficients are chosen from the sequence of Jacobsthal-Lucas numbers. We also present some identities about the known some fundamental identities such as the Cassini's, Catalan's and Vajda's identities.
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Congruences for $q$-Lucas Numbers
The Electronic Journal of Combinatorics, 2013 For $\alpha,\beta,\gamma,\delta\in{\mathbb Z}$ and ${\rm\nu}=(\alpha,\beta,\gamma,\delta)$, the $q$-Fibonacci numbers are given by$$F_0^{{\rm\nu}}(q)=0,\ F_1^{{\rm\nu}}(q)=1\text{ and }F_{n+1}^{{\rm\nu}}(q)=q^{\alpha n-\beta}F_{n}^{{\rm\nu}}(q)+q^{\gamma n-\delta}F_{n-1}^{{\rm\nu}}(q)\text{ for }n\geq 1.$$And define the $q$-Lucas number $L_{n}^{{\rm\nu}
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