Results 21 to 30 of about 255,151 (329)
Exact divisibility by powers of the integers in the Lucas sequence of the first kind
AIMS Mathematics, 2020 Lucas sequence of the first kind is an integer sequence $(U_n)_{n\geq0}$ which depends on parameters $a,b\in\mathbb{Z}$ and is defined by the recurrence relation $U_0=0$, $U_1=1$, and $U_n=aU_{n-1}+bU_{n-2}$ for $n\geq2$. In this article, we obtain exact
Kritkhajohn Onphaeng +1 more
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On members of Lucas sequences which are products of factorials [PDF]
, 2019 Here, we show that if $\{U_n\}_{n\ge 0}$ is a Lucas sequence, then the largest $n$ such that $|U_n|=m_1!m_2!\cdots m_k!$ with ...
Laishram, Shanta +2 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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On the reciprocal products of generalized Fibonacci sequences
Journal of Inequalities and Applications, 2022 In this paper, we use the properties of error estimation and the analytic method to study the reciprocal products of the bi-periodic Fibonacci sequence, the bi-periodic Lucas sequence, and the mth-order linear recursive sequence.
Tingting Du, Zhengang Wu
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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.
Koo, Lee Feng +3 more
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On some new results for the generalised Lucas sequences
Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2021 In this paper we introduce the functions which count the number of generalized Lucas and Pell-Lucas sequence terms not exceeding a given value x and, under certain conditions, we derive exact formulae (Theorems 3 and 4) and establish asymptotic limits ...
Andrica Dorin +2 more
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Identities relating six members of the Fibonacci family of sequences
Karpatsʹkì Matematičnì Publìkacìï, 2022 In this paper, we prove several identities each relating a sum of products of three terms coming from different members of the Fibonacci family of sequences with a comparable sum whose terms come from three other sequences.
R. Frontczak, T. Goy, M. Shattuck
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Complex Factorizations of the Lucas Sequences via Matrix Methods
Journal of Applied Mathematics, 2014 Firstly, we show a connection between the first Lucas sequence and the determinants of some tridiagonal matrices. Secondly, we derive the complex factorizations of the first Lucas sequence by computing those determinants with the help of Chebyshev ...
Honglin Wu
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On r-Jacobsthal and r-Jacobsthal-Lucas Numbers
Annales Mathematicae Silesianae, 2023 Recently, Bród introduced a new Jacobsthal-type sequence which is called r-Jacobsthal sequence in current study. After defining the appropriate r-Jacobsthal–Lucas sequence for the r-Jacobsthal sequence, we obtain some properties of these two sequences ...
Bilgici Göksal, Bród Dorota
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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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