Results 11 to 20 of about 248,402 (331)
The GCD Sequences of the Altered Lucas Sequences [PDF]
Annales Mathematicae Silesianae, 2020 In this study, we give two sequences {L+n}n≥1 and {L−n}n≥1 derived by altering the Lucas numbers with {±1, ±3}, terms of which are called as altered Lucas numbers.
Koken Fikri
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Coincidences in generalized Lucas sequences [PDF]
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.
Bravo, Eric F. +2 more
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Exceptional real Lucas sequences [PDF]
Pacific Journal of Mathematics, 1961 Lincoln Durst
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On a divisibility relation for Lucas sequences
Journal of Number Theory, 2016 In this note, we study the divisibility relation $U_m\mid U_{n+k}^s-U_n^s$, where ${\bf U}:=\{U_n\}_{n\ge 0}$ is the Lucas sequence of characteristic polynomial $x^2-ax\pm 1$ and $k,m,n,s$ are positive integers.
Yuri Bilu +4 more
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A generalization of Lucas polynomial sequence
Discrete Applied Mathematics, 2008 In this paper, we obtain a generalized Lucas polynomial sequence from the lattice paths for the Delannoy numbers by allowing weights on the steps (1,0),(0,1) and (1,1). These weighted lattice paths lead us to a combinatorial interpretation for such a Lucas polynomial sequence. The concept of Riordan arrays is extensively used throughout this paper.
Gi‐Sang Cheon +2 more
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Almost powers in the Lucas sequence [PDF]
Journal de Théorie des Nombres de Bordeaux, 2008 The {\it Lucas sequence} $(L_n)_{n\geq 0}$ is defined by $L_0=2, L_1=1$ and $L_n=L_{n-1}+L_{n-2}$ for $n\geq 2$. The first, third and fourth authors have proved, among other things, that the only perfect powers in the Lucas sequence are $L_1=1$ and $L_3=4$ [{\it Y. Bugeaud, M. Mignotte} and {\it S. Siksek}, Ann. Math. (2) 163, No.
Yann Bugeaud +3 more
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Lucas sequences and repdigits [PDF]
Mathematica Bohemica, 2021 Let $(G_n)_{n \geq1}$ be a binary linear recurrence sequence that is represented by the Lucas sequences of the first and second kind, which are $\{U_n\}$ and $\{V_n\}$, respectively. We show that the Diophantine equation $G_n=B \cdot(g^{lm}-1)/(g^l-1)$ has only finitely many solutions in $n, m \in\mathbb{Z}^+$, where $g \geq2$, $l$ is even and $1 \leq ...
Hayder Raheem Hashim, Szabolcs Tengely
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On the discriminator of Lucas sequences [PDF]
Annales mathématiques du Québec, 2018 We consider the family of Lucas sequences uniquely determined by $U_{n+2}(k)=(4k+2)U_{n+1}(k) -U_n(k),$ with initial values $U_0(k)=0$ and $U_1(k)=1$ and $k\ge 1$ an arbitrary integer. For any integer $n\ge 1$ the discriminator function $\mathcal{D}_k(n)$ of $U_n(k)$ is defined as the smallest integer $m$ such that $U_0(k),U_1(k),\ldots,U_{n-1}(k)$ are
Bernadette Faye +5 more
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Shifted powers in Lucas–Lehmer sequences [PDF]
Research in Number Theory, 2019 We develop a general framework for finding all perfect powers in sequences derived by shifting non-degenerate quadratic Lucas-Lehmer binary recurrence sequences by a fixed integer. By combining this setup with bounds for linear forms in logarithms and results based upon the modularity of elliptic curves defined over totally real fields, we are able to ...
Michael A. Bennett +2 more
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Elliptic Solutions of Dynamical Lucas Sequences [PDF]
Entropy, 2021 We study two types of dynamical extensions of Lucas sequences and give elliptic solutions for them. The first type concerns a level-dependent (or discrete time-dependent) version involving commuting variables. We show that a nice solution for this system is given by elliptic numbers. The second type involves a non-commutative version of Lucas sequences
Schlosser, Michael J., Yoo, Meesue
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