Results 81 to 90 of about 237,797 (205)
, 2013 In this short paper, we prove, by only using elementary tools, general cases when $U_n(P,Q) \neq \square$, where $U_n(P,Q)$ is the Lucas sequence of the first type.
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Geometric Aspects of Lucas Sequences, I
Tokyo Journal of Mathematics, 2020 This article is a sequel of $\langle$Geometric aspects of Lucas sequences, I$\rangle$, which presents a way of viewing Lucas sequences in the framework of group scheme theory. This enables us to treat the Lucas sequences from a geometric and functorial viewpoint, which was suggested by Laxton $\langle$On groups of linear recurrences, I$\rangle$ and by ...
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A Dynamical Property Unique to the Lucas Sequence
The Fibonacci Quarterly, 2001 9 ...
Puri, Y., Ward, T.
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The terms in Lucas sequences divisible by their indices [PDF]
, 2009 For Lucas sequences of the first kind (u_n) and second kind (v_n) defined as usual for positive n by u_n=(a^n-b^n)/(a-b), v_n=a^n+b^n, where a and b are either integers or conjugate quadratic integers, we describe the set of indices n for which n divides
Smyth, Chris
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Decomposition of terms in Lucas sequences
Journal of Logic and Analysis, 2009 Let N be any large integer. Proceeding directly to the factorization of N is not an easy task, even unfeasible unless N belongs to a particular family of integers. Then to surmount this major difficulty we might choose to ask about the factorization of an integer in a small neighborhood of N instead of N .
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Relationship between Vieta-Lucas polynomials and Lucas sequences
, 2022 Let $w_n=w_n(P,Q)$ be numerical sequences which satisfy the recursion relation \begin{equation*} w_{n+2}=Pw_{n+1}-Qw_n. \end{equation*} We consider two special cases $(w_0,w_1)=(0,1)$ and $(w_0,w_1)=(2,P)$ and we denote them by $U_n$ and $V_n$ respectively. Vieta-Lucas polynomial $V_n(X,1)$ is the polynomial of degree $n$.
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A trick around Fibonacci, Lucas and Chebyshev
, 2013 In this article, we present a trick around Fibonacci numbers which can be found in several magic books. It consists in computing quickly the sum of the successive terms of a Fibonacci-like sequence.
Lachal, Aimé
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A Note on Primality Testing Using Lucas Sequences [PDF]
, 1975 Michael A. Morrison
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Generalized Fibonacci and Lucas Sequences and Rootfinding Methods [PDF]
, 1993 Joseph B. Muskat
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International Journal of Mathematics and Mathematical Sciences, 1998 The Lucas sequence is defined by: L0=2,L1=1,Ln=Ln−1+Ln−2 for n≥2. Let V(n), r(n) denote respectively the number of partitions of n into parts, distinct parts from {Ln}. We develop formulas that facilitate the computation of V(n) and r(n).
Neville Robbins
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