Results 221 to 230 of about 31,122 (260)

On Concatenations of Fibonacci and Lucas Numbers

Bulletin of the Iranian Mathematical Society, 2022
Let \( (F_n)_{n\ge 0} \) and \( (L_n)_{n\ge 0} \) be the usual Fibonacci and Lucas sequences defined respectively by the linear recurrence relations: \( F_0=0 \), \( F_1=1 \), \( F_{n+2}=F_{n+1}+F_n \) and \( L_0=2 \), \( L_1=1 \), \( L_{n+2}=L_{n+1}+L_n \) for all \( n\ge 0 \).
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On quaternion‐Gaussian Lucas numbers

Mathematical Methods in the Applied Sciences, 2020
In this study, we have considered Gaussian Lucas numbers and given the properties of these numbers. Then, we have defined the quaternions that accept these numbers as coefficients. We have examined whether the numbers defined provide some identities for quaternions in the literature.
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Fibonacci and Lucas numbers which are product of two Jacobsal-Lucas numbers

2023
In this study, we find all Fibonacci numbers F-k and Lucas numbers L-k which are products of two Jacobsthal-Lucas numbers. More generally, taking k, m, n as nonnegative integers, we proved that F-k = j(m)j(n) = (2(m) + ((-1)(m)) . (2(n) + ((-1)(n)) implies that (k, m, n) = (1, 1, 1); (2, 1, 1), (3, 0, 1), (5, 1, 2), (9, 0, 4) and L-k = j(m)j(n) implies
Erduvan, F, Keskin, R
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Lucas' number is finally up

Journal of Philosophical Logic, 1982
Discussion de l'argumentation de J. R. Lucas suivant laquelle les etres humains ne peuvent etre des machines ("Minds, Machines and Godel", Philosophy, 36, 1961, p. 120-124). L'A. montre que l'argument de Lucas suivant lequel il n'est pas une machine repose sur une premisse erronee: suivant l'A., Lucas est donc lui-meme une machine.
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Fibonacci and Lucas Numbers

2021
In the literature, the Fibonacci numbers are usually denoted by \(F_n\), but this symbol is already reserved for the Fermat numbers in this book. So we will denote them by \(K_n\). The sequence of Fibonacci numbers \(\,\,(K_n)_{n=0}^\infty \,\,\) starts with \(K_0=0\) and \(K_1=1\) and satisfies the recurrence.
Michal Křížek, Lawrence Somer, Alena Šolcová   +2 more
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Perfect fibonacci and lucas numbers

Rendiconti del Circolo Matematico di Palermo, 2000
Using elementary means, the author shows that no Fibonacci or Lucas number is perfect.
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On Square Pseudo-Lucas Numbers

Canadian Mathematical Bulletin, 1978
J. H. E. Cohn (1) has shown thatare the only square Fibonacci numbers in the set of Fibonacci numbers defined byIf n is a positive integer, we shall call the numbers defined by(1)pseudo-Lucas numbers.
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Coding theory on Lucas p numbers

Discrete Mathematics, Algorithms and Applications, 2016
In [K. Kuhapatanakul, The Lucas [Formula: see text]-matrix, Internat. J. Math. Ed. Sci. Tech. (2015), http://dx.doi.org/10.1080/0020739X.2015.1026612], Kuhapatanakul introduced Lucas [Formula: see text] matrix, [Formula: see text] whose elements are Lucas [Formula: see text] numbers. In this paper, we developed a new coding and decoding method followed
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Trisection method by k-Lucas numbers

Applied Mathematics and Computation, 2008
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Mersenne numbers as a difference of two Lucas numbers

Commentationes Mathematicae Universitatis Carolinae, 2023
Summary: Let \((L_n)_{n\geq 0}\) be the Lucas sequence. We show that the Diophantine equation \(L_n-L_m=M_k\) has only the nonnegative integer solutions \((n,m,k)=(2,0,1)\), \((3,1,2)\), \((3,2,1)\), \((4,3,2)\), \((5,3,3)\), \((6,2,4)\), \((6,5,3)\) where \(M_k=2^k-1\) is the \(k\)th Mersenne number and \(n>m\).
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