Results 31 to 40 of about 242,259 (303)
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
core +1 more source
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
doaj +1 more source
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
core +2 more sources
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
openaire +2 more sources
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
doaj +1 more source
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
doaj +1 more source
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
doaj +1 more source
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
doaj +1 more source
A method for computing Lucas sequences
Computers & Mathematics with Applications, 1999 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Chin-Chen Chang +2 more
openaire +2 more sources
A lucas based cryptosystem analog to the ElGamal cryptosystem and elliptic curve cryptosystem [PDF]
, 2014 In this paper, a new cryptosystem will be developed which is analogue to ElGamal encryption scheme and based on Lucas sequence in the elliptic curve group over finite field. In this encryption scheme, an Elliptic curve Diffie-Hellman (ECDH) key agreement
Koo, Lee Feng +3 more
core +1 more source