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Repdigits as difference of two Fibonacci or Lucas numbers
Математичні Студії, 2021 In the present study we investigate all repdigits which are expressed as a difference of two Fibonacci or Lucas numbers. We show that if $F_{n}-F_{m}$ is a repdigit, where $F_{n}$ denotes the $n$-th Fibonacci number, then $(n,m)\in \{(7,3),(9,1),(9,2 ...
P. Ray, K. Bhoi
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Oscillatory Nonautonomous Lucas Sequences [PDF]
International Journal of Differential Equations, 2009 The oscillatory behavior of the solutions of the second‐order linear nonautonomous equation x(n + 1) = a(n)x(n) − b(n)x(n − 1), n ∈ ℕ0, where a, b : ℕ0 → ℝ, is studied. Under the assumption that the sequence b(n) dominates somehow a(n), the amplitude of the oscillations and the asymptotic behavior of its solutions are also analized.
Ferreira, José M., Pinelas, Sandra
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Diophantine equations with Lucas and Fibonacci number coefficients [PDF]
Notes on Number Theory and Discrete MathematicsFibonacci and Lucas numbers are special number sequences that have been the subject of many studies throughout history due to the relations they provide.
Cemil Karaçam +3 more
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Additional Fibonacci-Bernoulli relations
Researches in Mathematics, 2022 We continue our study on relationships between Fibonacci (Lucas) numbers and Bernoulli numbers and polynomials. The derivations of our results are based on functional equations for the respective generating functions, which in our case are combinations ...
K. Adegoke, R. Frontczak, T.P. Goy
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Coincidences in Generalized Lucas Sequences
The Fibonacci Quarterly, 2014 For an integer $k\geq 2$, let $(L_{n}^{(k)})_{n}$ be the $k-$generalized Lucas sequence which starts with $0,\ldots,0,2,1$ ($k$ terms) and each term afterwards is the sum of the $k$ preceding terms. In this paper, we find all the integers that appear in different generalized Lucas sequences; i.e., we study the Diophantine equation $L_n^{(k)}=L_m^{(\ell)
Bravo, Eric F. +2 more
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On the Monoid Generated by a Lucas Sequence [PDF]
, 2017 A Lucas sequence is a sequence of the general form $v_n = (ϕ^n - \barϕ^n)/(ϕ-\barϕ)$, where $ϕ$ and $\barϕ$ are real algebraic integers such that $ϕ+\barϕ$ and $ϕ\barϕ$ are both rational. Famous examples include the Fibonacci numbers, the Pell numbers, and the Mersenne numbers.
Heuberger, Clemens, Wagner, Stephan
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An analysis for chosen plaintext attack in elliptic curve cryptosystem based on second order lucas sequence [PDF]
, 2019 Elliptic Curve Cryptography is a cryptography based on the algebraic structure of elliptic curves over finite fields. The security of Elliptic Curve Cryptography depends on discrete logarithms that is much more difficult to challenge at equivalent key ...
Naning @ Zin, Fatin Hana +4 more
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Almost repdigits in balancing and Lucas-balancing sequences [PDF]
Notes on Number Theory and Discrete MathematicsIn this paper, we define the notion of almost repdigit as a positive integer whose digits are all equal except for at most one digit, and we search all terms of the balancing and Lucas-balancing sequences which are almost repdigits.
Manasi K. Sahukar, Hussain Basha
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Aperiodic Diffractive Lenses Based on Lucas and Pell–Lucas Sequences for Controlled Multifocal Optical Fields [PDF]
EPJ Web of Conferences. In this work, two families of sequence-based diffractive lenses are presented and comparatively analyzed: Lucas diffractive lenses and Pell– Lucas diffractive lenses.
Furlan Walter D. +4 more
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Some properties of the generalized (p,q)- Fibonacci-Like number
MATEC Web of Conferences, 2018 For the real world problems, we use some knowledge for explain or solving them. For example, some mathematicians study the basic concept of the generalized Fibonacci sequence and Lucas sequence which are the (p,q) – Fibonacci sequence and the (p,q ...
Suvarnamani Alongkot
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