Results 71 to 80 of about 237,797 (205)

Horadam–Lucas Cubes

Axioms
In this paper, we introduce a novel class of graphs referred to as the Horadam–Lucas cubes. This class extends the concept of Lucas cubes and retains numerous desirable properties associated with them.
Elif Tan, Luka Podrug, Vesna Iršič Chenoweth   +2 more
doaj   +1 more source

Primitive Divisors of Lucas and Lehmer Sequences [PDF]

Mathematics of Computation, 1995
In this paper we prove that if n>30 030, then the nth element of any Lucas or Lehmer sequence has a primitive divisor.
openaire   +10 more sources

On fourth-order jacobsthal quaternions

Journal of Mathematical Sciences and Modelling, 2018
In this paper, we present for the first time a sequence of quaternions of order 4 that we will call the fourth-order Jacobsthal and the fourth-order Jacobsthal-Lucas quaternions. In particular, we are interested in the generating function, Binet formula,
Gamaliel Cerda-morales
doaj   +1 more source

Generalized Fibonacci-Lucas Sequence [PDF]

Turkish Journal of Analysis and Number Theory, 2014
The Fibonacci sequence is a source of many nice and interesting identities. A similar interpretation exists for Lucas sequence. The Fibonacci sequence, Lucas numbers and their generalization have many interesting properties and applications to almost every field.
Bijendra Singh, Omprakash Sikhwal, Yogesh Kumar Gupta   +2 more
openaire   +1 more source

On Diophantine equations involving Lucas sequences

Open Mathematics, 2019
In this paper, we shall study the Diophantine equation un = R(m)P(m)Q(m), where un is a Lucas sequence and R, P and Q are polynomials (under weak assumptions).
Trojovský Pavel
doaj   +1 more source

A Matrix Approach for Divisibility Properties of the Generalized Fibonacci Sequence

Discrete Dynamics in Nature and Society, 2013
We give divisibility properties of the generalized Fibonacci sequence by matrix methods. We also present new recursive identities for the generalized Fibonacci and Lucas sequences.
Aynur Yalçiner
doaj   +1 more source

The power sum of balancing polynomials and their divisible properties

AIMS Mathematics
In recent years, many scholars have studied the division properties of polynomials and sequence power sums. In this paper, we use Girard-Waring formula and combinatorial method to study the power sum problem of balancing polynomials and Lucas-balancing ...
Hong Kang
doaj   +1 more source

Lucas congruences for the Ap\'ery numbers modulo $p^2$

, 2020
The sequence $A(n)_{n \geq 0}$ of Ap\'ery numbers can be interpolated to $\mathbb{C}$ by an entire function. We give a formula for the Taylor coefficients of this function, centered at the origin, as a $\mathbb{Z}$-linear combination of multiple zeta ...
Krattenthaler, Christian, Rowland, Eric, Yassawi, Reem   +2 more
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DETERMINANTAL IDENTITIES FOR k LUCAS SEQUENCE

Journal of New Theory, 2016
Abstaract−In this paper, we defined new relationship between k Lucas sequences and determi- nants of their associated matrices, this approach is different and never tried in k Fibonacci sequence ...
Ashok Dnyandeo Godase, Machindra Baban Dhakne   +1 more
doaj  

On the equilibrium in a discrete-time Lucas Model [PDF]

In this paper I study a discrete-time version of the Lucas model with the endogenous leisure but without physical capital. Under standard conditions I prove that the optimal human capital sequence is increasing.
Marius Boldea
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