Results 41 to 50 of about 145,594 (304)
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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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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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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The Anatomical Record, EarlyView., 2023 Abstract Based on histological cross‐sections, the chondrocranium of the common musk turtle (Sternotherus odoratus) was reconstructed, described, and compared with other turtles. It differs from that of other turtle chondrocrania by possessing elongated, slightly dorsally orientated nasal capsules with three dorsolateral foramina, which might be ...
Luca Leicht +2 more
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Practical numbers in Lucas sequences [PDF]
Quaestiones Mathematicae, 2018 A practical number is a positive integer n such that all the positive integers m ≤ n can be written as a sum of distinct divisors of n. Let (un)n≥0 be the Lucas sequence satisfying u0 = 0, u1 = 1, and un+2 = aun+1 + bun for all integers n ≥ 0, where a and b are fixed nonzero integers. Assume a(b + 1) even and a 2 + 4b > 0.
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On Bicomplex Jacobsthal-Lucas Numbers
Journal of Mathematical Sciences and Modelling, 2020 In this study we introduced a sequence of bicomplex numbers whose coefficients are chosen from the sequence of Jacobsthal-Lucas numbers. We also present some identities about the known some fundamental identities such as the Cassini's, Catalan's and ...
Serpil Halıcı
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A method for computing Lucas sequences
Computers & Mathematics with Applications, 1999 AbstractMost of public-key cryptosystems rely on one-way functions, which can be used to encrypt and sign messages. Their encryption and signature operations are based on the computation of exponentiation. Recently, some public-key cryptosystems are proposed and based on Lucas functions, and the Lucas sequences are performed as S = V(d)modN.
Chin-Chen Chang +2 more
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Mersenne-Horadam identities using generating functions
Karpatsʹkì Matematičnì Publìkacìï, 2020 The main object of the present paper is to reveal connections between Mersenne numbers $M_n=2^n-1$ and generalized Fibonacci (i.e., Horadam) numbers $w_n$ defined by a second order linear recurrence $w_n=pw_{n-1}+qw_{n-2}$, $n\geq 2$, with $w_0=a$ and ...
R. Frontczak, T.P. Goy
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On $k$-Fibonacci balancing and $k$-Fibonacci Lucas-balancing numbers
Karpatsʹkì Matematičnì Publìkacìï, 2021 The balancing number $n$ and the balancer $r$ are solution of the Diophantine equation $$1+2+\cdots+(n-1) = (n+1)+(n+2)+\cdots+(n+r). $$ It is well known that if $n$ is balancing number, then $8n^2 + 1$ is a perfect square and its positive square root is
S.E. Rihane
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Some properties of the generalized (p,q)- Fibonacci-Like number
MATEC Web of Conferences, 2018 For the real world problems, we use some knowledge for explain or solving them. For example, some mathematicians study the basic concept of the generalized Fibonacci sequence and Lucas sequence which are the (p,q) – Fibonacci sequence and the (p,q ...
Suvarnamani Alongkot
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