Results 11 to 20 of about 145,594 (304)
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
openalex +4 more sources
On Squares in Lucas Sequences [PDF]
arXiv, 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.
arxiv +3 more sources
The eccentricity sequences of Fibonacci and Lucas cubes
Discrete Mathematics, 2011 AbstractThe Fibonacci cube Γn is the subgraph of the hypercube induced by the binary strings that contain no two consecutive 1’s. The Lucas cube Λn is obtained from Γn by removing vertices that start and end with 1. The eccentricity of a vertex u, denoted eG(u) is the greatest distance between u and any other vertex v in the graph G. For a given vertex
Aline Castro, Michel Mollard
openalex +4 more sources
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
openalex +6 more sources
Exceptional real Lucas sequences [PDF]
Pacific Journal of Mathematics, 1961 Lincoln Durst
openalex +4 more sources
Primitive Divisors of Lucas Sequences in Polynomial Rings [PDF]
arXivIt is known that all terms $U_n$ of a classical regular Lucas sequence have a primitive prime divisor if $n>30$. In addition, a complete description of all regular Lucas sequences and their terms $U_n$, $2\leq n\leq 30$, which do not have a primitive divisor is also known.
J. Conceição
arxiv +3 more sources
A Sequence Bounded Above by the Lucas Numbers
Sakarya Üniversitesi Fen Bilimleri Enstitüsü Dergisi, 2018 In this work, we consider the sequence whosenthterm isthe number of h-vectors of length n. The set of integer vectors E(n)isintroduced. For, n>=2,the cardinality ofE(n)is the nthLucasnumber Lnisshowed.
Ali Aydoğdu +2 more
doaj +5 more sources
A generalization of Lucas sequence and associated identities
Boletim da Sociedade Paranaense de Matemática, 2022 In this paper, we attempt to generalize Lucas sequence by generating certain number of sequences whose terms are obtained by adding the last two generated terms of the preceding sequence.
Neeraj Kumar Paul, Helen K. Saikia
doaj +1 more source
Blocks within the period of Lucas sequence
Ratio Mathematica, 2021 In this paper, we consider the periodic nature of the sequence of Lucas numbers L_n defined by the recurrence relation L_n= L_(n-1)+L_(n-2); for all n≥2; with initial condition L_0=2 and L_1=1.
Rima P. Patel, Dr. Devbhadra V. Shah
doaj +1 more source
Lucas difference sequence spaces defined by Orlicz function in 2-normed spaces
Demonstratio MathematicaIn this article, we introduce new sequence spaces defined via an Orlicz function within the framework of a 2-normed space and incorporating the Lucas difference matrix and its associated matrix domain.
Cai Qing-Bo +3 more
doaj +2 more sources