Results 71 to 80 of about 8,726 (124)

On the Existence of Solutions of Diophantine Equations Related to Subbalancing Numbers

Journal of Mathematics, Volume 2025, Issue 1, 2025.
In this paper, we introduce a new sequence of subbalancing numbers by considering balancing numbers as the values of D in the Diophantine equations provided by subbalancing numbers. For this, first we prove that when the values of the positive integer D are chosen as balancing numbers, there exist integer solutions of the Diophantine equations that ...
Selin Sarı, Gül Karadeniz-Gözeri, Pramita Mishra   +2 more
wiley   +1 more source

Novel Classes on Generating Functions of the Products of (p,q)-Modified Pell Numbers with Several Bivariate Polynomials

Mathematics
In this paper, using the symmetrizing operator δe1e22−l, we derive new generating functions of the products of p,q-modified Pell numbers with various bivariate polynomials, including Mersenne and Mersenne Lucas polynomials, Fibonacci and Lucas ...
Ali Boussayoud, Salah Boulaaras, Ali Allahem   +2 more
doaj   +1 more source

A New Generalization of Leonardo Sequences: Biperiodic Leonardo Sequence

Journal of Mathematics, Volume 2025, Issue 1, 2025.
In this study, we define a new type of number sequence called biperiodic Leonardo sequence by the recurrence relation Lena,b=aLen−1+Len−2+1 (for even n) and Lena,b=bLen−1+Len−2+1 (for odd n) with the initial conditions Le0a,b=Le1a,b=1. We obtained the characteristic function, generating function, and Binet’s formula for this sequence and propose a ...
Hasan Gökbaş, Mohammad W. Alomari
wiley   +1 more source

On the Balancing-bilinear system of difference equations: solutions via some number sequences and global stability

Miskolc Mathematical Notes
In the current paper, we present a new class of systems called the Balancing-bilinear system of difference equations to investigate some theoretical proprieties.
Ahmed Ghezal, Imane Zemmouri
doaj   +1 more source

Numerical solutions and simulations of the fractional COVID‐19 model via Pell–Lucas collocation algorithm

Mathematical Methods in the Applied Sciences, Volume 47, Issue 18, Page 14457-14475, December 2024.
The aim of this study is to present the evolution of COVID‐19 pandemic in Turkey. For this, the SIR (Susceptible, Infected, Removed) model with the fractional order derivative is employed. By applying the collocation method via the Pell–Lucas polynomials (PLPs) to this model, the approximate solutions of model with fractional order derivative are ...
Gamze Yıldırım, Şuayip Yüzbaşı
wiley   +1 more source

Repdigits as Products of Consecutive Pell or Pell–Lucas Numbers

Iranian Journal of Mathematical Sciences and Informatics
Summary: A positive integer is called a repdigit if it has only one distinct digit in its decimal expansion. In this paper, we find all repdigits that are products of consecutive Pell or Pell-Lucas numbers. This paper continues previous work which dealt with finding occurrences of repdigits in the Pell and Pell-Lucas sequences.
Bravo, Eric F., Bravo, Jhon J.
openaire   +2 more sources

Gaussian-Hybrid Numbers Obtained From Pell and Pell-Lucas Sequences

Journal of Advances in Mathematics and Computer Science, 2022
In this study, we define a new type of Pell and Pell-Lucas numbers which are called Gaussian-hybrid Pell and Pell-Lucas numbers. We also give negaGaussian-hybrid Pell and Pell-Lucas numbers, the characteristic number and the type number of Gaussian-hybrid Pell and Pell-Lucas numbers.
openaire   +1 more source

Genetic erosion in domesticated barley and a hypothesis of a North African centre of diversity

Ecology and Evolution, Volume 14, Issue 8, August 2024.
Barley cultivated 6 millennia ago was more diverse than extant cultivars and landraces. Private variants and chloroplast haplotypes indicate strong genetic erosion in North Africa and link together ancient barley, extant Ethiopian landraces and a rudimentary wild population of Cyrenaica.
Peter Civáň, Agostino Fricano, Joanne Russell, Caroline Pont, Hakan Özkan, Benjamin Kilian, Terence A. Brown   +6 more
wiley   +1 more source

Pell and Pell–Lucas Sequences of Fractional Order

Fractal and Fractional
The purpose of this paper is to introduce the fractional Pell numbers, together with several properties, via a Grünwald–Letnikov fractional operator of orders q∈(0,1) and q∈(1,2).
Jagan Mohan Jonnalagadda, Marius-F. Danca   +1 more
doaj   +1 more source

Convolutions of the generalized Pell and Pell-Lucas numbers

Filomat, 2016
We consider the convolution of the generalized Pell numbers-P(s) n,m and the convolution of the generalized Pell-Lucas numbers-Q(s) n,m. For s = 0, the sequence P(0) n,m represents the generalized Pell numbers Pn;m, and the sequence Q(0) n,m represents the generalized Pell-Lucas numbers Qn,m ([1], [2]). For m = 2 and s = 0, the numbers P(0)
openaire   +1 more source