Results 81 to 90 of about 613 (205)
Strong divisibility sequences and sieve methods
Mathematika, Volume 70, Issue 4, October 2024.Abstract We investigate strong divisibility sequences and produce lower and upper bounds for the density of integers in the sequence that only have (somewhat) large prime factors. We focus on the special cases of Fibonacci numbers and elliptic divisibility sequences, discussing the limitations of our methods.
Tim Browning, Matteo Verzobio
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The Third Order Jacobsthal Octonions: Some Combinatorial Properties
Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2018 Various families of octonion number sequences (such as Fibonacci octonion, Pell octonion and Jacobsthal octonion) have been established by a number of authors in many di erent ways.
Cerda-Morales Gamaliel
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Multiplicative dependence of k-Fibonacci numbers with the Fibonacci, Lucas, and Pell sequences
The Ramanujan JournalAbstract The k –generalized Fibonacci sequence $$(F_m^{(k)})_{m\ge 2-k}$$ (
Gómez, C, C. Gómez, J, Luca, F
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On the Periods of Biperiodic Fibonacci and Biperiodic Lucas Numbers
Discrete Dynamics in Nature and Society, 2016 This paper is concerned with periods of Biperiodic Fibonacci and Biperiodic Lucas sequences taken as modulo prime and prime power. By using Fermat’s little theorem, quadratic reciprocity, many results are obtained.
Dursun Tascı, Gul Ozkan Kızılırmak
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The sequences of Fibonacci and Lucas for quadratic fields
Boletim da Sociedade Paranaense de MatemáticaWe construct the sequences of Fibonacci and Lucas in any quadratic field $\mathbb{Q}(\sqrt{d}\,)$ with $d>0$ square free, noting that the general properties remain valid as those given by the classical sequences of Fibonacci and Lucas for the case $d = 5$, under the respective variants.
Pablo Lam-Estrada +5 more
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An Extensive Review of the Literature Using the Diophantine Equations to Study Fuzzy Set Theory
International Journal of Mathematics and Mathematical Sciences, Volume 2024, Issue 1, 2024.Every field in mathematics has made significant progress in research with fuzzy sets. Numerous application fields were discovered in both empirical and theoretical investigations, ranging from information technology to medical technology, from the natural sciences to the physical sciences, and from technical education to fine arts education.
K. M. Abirami +4 more
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Fibonacci and Lucas sequences at negative indices
, 2014 This study investigate the Fibonacci and Lucas sequences at neg- ative indices. In this paper we give the formulas of F????(nk+r) and L????(nk+r) depending on whether the indices are odd or even. For this purpose we con- sider a special matrix and we give various combinatorial identities related with the Fibonacci and Lucas sequences by using the ...
Halıcı, Serpil, Akyüz, Zeynep
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International Journal of Mathematics and Mathematical Sciences, Volume 2024, Issue 1, 2024.Some boundedness and convergence properties of generalized Fibonacci’s‐type recurrences and their associated iterated recurrence ratios between pairs of consecutive terms are discussed under a wide number of initial conditions. Also, a more general, so‐called (k, q) Fibonacci’s recurrence and the associated Fibonacci’s ratio recurrences are ...
Manuel De la Sen, V. Ravichandran
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A quantum calculus framework for Gaussian Fibonacci and Gaussian Lucas quaternion numbers [PDF]
Notes on Number Theory and Discrete MathematicsIn order to investigate the relationship between Gaussian Fibonacci numbers and quantum numbers and to develop both a deeper theoretical understanding in this study, q-Gaussian Fibonacci, q-Gaussian Lucas quaternions and polynomials are taken with ...
Bahar Kuloğlu
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Journal of Mathematics, Volume 2024, Issue 1, 2024.Spinors can be expressed as Lie algebra of infinitesimal rotations. Spinors are also defined as elements of a vector space which carries a linear representation of the Clifford algebra typically. The motivation for this study is to define a new and particular sequence.
Tülay Erişir, Serkan Araci
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