Results 41 to 50 of about 31,545 (292)
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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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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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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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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A method to decrease computation time for fourth order Lucas sequence [PDF]
, 2013 The fourth order Lucas sequence is a linear recurrence relation related to quartic polynomial and based on Lucas function. This sequence had been used to develop the LUC4,6 cryptosystem.
Wong Tze Jin +7 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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Some Polynomial Sequence Relations
Mathematics, 2019 We give some polynomial sequence relations that are generalizations of the Sury-type identities. We provide two proofs, one based on an elementary identity and the other using the method of generating functions.
Chan-Liang Chung
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Mersenne-Horadam identities using generating functions
Karpatsʹkì Matematičnì Publìkacìï, 2020 The main object of the present paper is to reveal connections between Mersenne numbers $M_n=2^n-1$ and generalized Fibonacci (i.e., Horadam) numbers $w_n$ defined by a second order linear recurrence $w_n=pw_{n-1}+qw_{n-2}$, $n\geq 2$, with $w_0=a$ and ...
R. Frontczak, T.P. Goy
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On $k$-Fibonacci balancing and $k$-Fibonacci Lucas-balancing numbers
Karpatsʹkì Matematičnì Publìkacìï, 2021 The balancing number $n$ and the balancer $r$ are solution of the Diophantine equation $$1+2+\cdots+(n-1) = (n+1)+(n+2)+\cdots+(n+r). $$ It is well known that if $n$ is balancing number, then $8n^2 + 1$ is a perfect square and its positive square root is
S.E. Rihane
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On New Polynomial Sequences Constructed to Each Vertex in an n-Gon
Discrete Dynamics in Nature and Society, 2022 In this work, we bring to light the properties of newly formed polynomial sequences at each vertex of Pell polynomial sequences placed clockwise at each vertex in the n-gon. We compute the relation among the polynomials with such vertices.
Abdul Hamid Ganie +3 more
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