Results 31 to 40 of about 237,797 (205)
ON PERFECT POWERS IN LUCAS SEQUENCES [PDF]
International Journal of Number Theory, 2005 Let (un)n≥0be the binary recurrence sequence of integers given by u0= 0, u1= 1 and un+2= 2(un+1+ un). We show that the only positive perfect powers in this sequence are u1= 1 and u4= 16. We further discuss the problem of determining perfect powers in Lucas sequences in general.
Bugeaud, Yann +3 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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On the intersections of Fibonacci, Pell, and Lucas numbers [PDF]
, 2010 We describe how to compute the intersection of two Lucas sequences of the forms $\{U_n(P,\pm 1) \}_{n=0}^{\infty}$ or $\{V_n(P,\pm 1) \}_{n=0}^{\infty}$ with $P\in\mathbb{Z}$ that includes sequences of Fibonacci, Pell, Lucas, and Lucas-Pell numbers.
Bilu +13 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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The first map of crop sequence types in Europe over 2012–2018 [PDF]
Earth System Science Data, 2023 Crop diversification is considered a key element of agroecological transition, whereas current dominant cropping systems are known to rely on only a few crop species – like cereals in Europe.
R. Ballot, N. Guilpart, M.-H. Jeuffroy
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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 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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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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Exact divisibility by powers of the integers in the Lucas sequences of the first and second kinds
AIMS Mathematics, 2021 Lucas sequences of the first and second kinds are, respectively, the integer sequences $ (U_n)_{n\geq0} $ and $ (V_n)_{n\geq0} $ depending on parameters $ a, b\in\mathbb{Z} $ and defined by the recurrence relations $ U_0 = 0 $, $ U_1 = 1 $, and $ U_n ...
Kritkhajohn Onphaeng +1 more
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