Special Issue "New Insights in Algebra, Discrete Mathematics, and Number Theory"

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Algebraic Geometry".

Deadline for manuscript submissions: 31 January 2021.

Special Issue Editors

Dr. Pavel Trojovský
Website SciProfiles
Guest Editor
Department of Mathematics, Faculty of Science, University of Hradec Králové, 500 03 Hradec Králové, Czech Republic
Interests: number theory, linear algebra, difference equations, computer-aided mathematics
Prof. Dr. Diego Marques
Website
Guest Editor
Department of Mathematics, University of Brasilia, L2 Norte, Asa Norte 70910-900 - Brasilia, Brazil
Interests: transcendental number theory, Diophantine equations, recurrent sequences, Diophantine approximation, elementary number theory
Prof. Dr. Iwona Włoch
Website
Guest Editor
Rzeszów University of Technology, Faculty of Mathematics and Applied Physics, al. Powstańców Warszawy 12, 35-359 Rzeszów, Poland
Interests: discrete mathematics, graph theory, number theory

Special Issue Information

Dear Colleagues,

We all probably realize, as we study the current breakthrough results in our favorite area of mathematics, that the very different areas of mathematics are now approaching each other again thanks to the baseline realization that other discipline methods are crucial of proof assertions in our field of mathematics. The purpose of this Special Issue is to gather a collection of articles reflecting new trends in contemporary elementary, abstract, linear, Boolean, commutative, computer and homological algebra, analytical, algebraic, combinatorial and computational number theory, modular forms, factors, fractions, arithmetic dynamics, sieve methods, quadratic forms, L-functions, combinatorics and graph theory. In this Special Issue, we welcome original research articles or review articles focused on recent problems concerning mainly to abstract and linear algebra, algebraic, analytic and combinatorial number theory, combinatorics and graph theory as well as their multidisciplinary applications.

Dr. Pavel Trojovský
Prof. Dr. Diego Marques
Prof. Dr. Iwona Włoch
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All papers will be peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Mathematics is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 1200 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • Special groups, rings and fields
  • Applications of Linear algebra
  • Algebraic number fields
  • Transcendental number theory
  • Arithmetic functions
  • Diophantine equations and Diophantine approximations
  • Recurrence sequences and difference equations
  • Combinatorics
  • Directed, discrete and planar graphs

Published Papers (3 papers)

Order results
Result details
Select all
Export citation of selected articles as:

Research

Open AccessArticle
Some Diophantine Problems Related to k-Fibonacci Numbers
Mathematics 2020, 8(7), 1047; https://doi.org/10.3390/math8071047 - 30 Jun 2020
Abstract
Let k1 be an integer and denote (Fk,n)n as the k-Fibonacci sequence whose terms satisfy the recurrence relation Fk,n=kFk,n1+Fk, [...] Read more.
Let k 1 be an integer and denote ( F k , n ) n as the k-Fibonacci sequence whose terms satisfy the recurrence relation F k , n = k F k , n 1 + F k , n 2 , with initial conditions F k , 0 = 0 and F k , 1 = 1 . In the same way, the k-Lucas sequence ( L k , n ) n is defined by satisfying the same recursive relation with initial values L k , 0 = 2 and L k , 1 = k . The sequences ( F k , n ) n 0 and ( L k , n ) n 0 were introduced by Falcon and Plaza, who derived many of their properties. In particular, they proved that F k , n 2 + F k , n + 1 2 = F k , 2 n + 1 and F k , n + 1 2 F k , n 1 2 = k F k , 2 n , for all k 1 and n 0 . In this paper, we shall prove that if k > 1 and F k , n s + F k , n + 1 s ( F k , m ) m 1 for infinitely many positive integers n, then s = 2 . Similarly, that if F k , n + 1 s F k , n 1 s ( k F k , m ) m 1 holds for infinitely many positive integers n, then s = 1 or s = 2 . This generalizes a Marques and Togbé result related to the case k = 1 . Furthermore, we shall solve the Diophantine equations F k , n = L k , m , F k , n = F n , k and L k , n = L n , k . Full article
(This article belongs to the Special Issue New Insights in Algebra, Discrete Mathematics, and Number Theory)
Open AccessArticle
A Quadratic Diophantine Equation Involving Generalized Fibonacci Numbers
Mathematics 2020, 8(6), 1010; https://doi.org/10.3390/math8061010 - 20 Jun 2020
Abstract
The sequence of the k-generalized Fibonacci numbers (Fn(k))n is defined by the recurrence Fn(k)=j=1kFnj(k) beginning with the k [...] Read more.
The sequence of the k-generalized Fibonacci numbers ( F n ( k ) ) n is defined by the recurrence F n ( k ) = j = 1 k F n j ( k ) beginning with the k terms 0 , , 0 , 1 . In this paper, we shall solve the Diophantine equation F n ( k ) = ( F m ( l ) ) 2 + 1 , in positive integers m , n , k and l. Full article
(This article belongs to the Special Issue New Insights in Algebra, Discrete Mathematics, and Number Theory)
Open AccessArticle
On the Growth of Some Functions Related to z(n)
Mathematics 2020, 8(6), 876; https://doi.org/10.3390/math8060876 - 01 Jun 2020
Abstract
The order of appearance z:Z>0Z>0 is an arithmetic function related to the Fibonacci sequence (Fn)n. This function is defined as the smallest positive integer solution of the congruence Fk [...] Read more.
The order of appearance z : Z > 0 Z > 0 is an arithmetic function related to the Fibonacci sequence ( F n ) n . This function is defined as the smallest positive integer solution of the congruence F k 0 ( mod n ) . In this paper, we shall provide lower and upper bounds for the functions n x z ( n ) / n , p x z ( p ) and p r x z ( p r ) . Full article
(This article belongs to the Special Issue New Insights in Algebra, Discrete Mathematics, and Number Theory)
Show Figures

Figure 1

Back to TopTop