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The Integer Valued Polynomials On Lucas Numbers

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The Integer Valued Polynomials On Lucas Numbers

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Author : Amitabh Kumer Halder
language : en
Publisher:
Release Date : 2017

The Integer Valued Polynomials On Lucas Numbers written by Amitabh Kumer Halder and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017 with categories.

An integer-valued polynomial on a subset, S, of the set of integers, Z, is a polynomial f(x) 2 Q[x] such that f(S) Z. The collection, Int(S;Z), of such integer-valued polynomials forms a ring with many interesting properties. The concept of p-ordering and the associated p-sequence due to Bhargava [2] is used for nding integer-valued polynomials on any subset, S, of Z. In this thesis, we concentrate on extending the work of Keith Johnson and Kira Scheibelhut [14] for the case S = L, the Lucas numbers, where they work on integervalued polynomials on S = F, Fibonacci numbers. We also study integer-valued polynomials on the general 3 term recursion sequence, G, of integers for a given pair of initial values with some interesting properties. The results are well-agreed with those of [14].

The Lucas Sequences

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Author : Christian J.-C. Ballot
language : en
Publisher: Springer Nature
Release Date : 2023-10-19

The Lucas Sequences written by Christian J.-C. Ballot and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-10-19 with Mathematics categories.

Although the Lucas sequences were known to earlier investigators such as Lagrange, Legendre and Genocchi, it is because of the enormous number and variety of results involving them, revealed by Édouard Lucas between 1876 and 1880, that they are now named after him. Since Lucas’ early work, much more has been discovered concerning these remarkable mathematical objects, and the objective of this book is to provide a much more thorough discussion of them than is available in existing monographs. In order to do this a large variety of results, currently scattered throughout the literature, are brought together. Various sections are devoted to the intrinsic arithmetic properties of these sequences, primality testing, the Lucasnomials, some associated density problems and Lucas’ problem of finding a suitable generalization of them. Furthermore, their application, not only to primality testing, but also to integer factoring, efficient solution of quadratic and cubic congruences, cryptography and Diophantine equations are briefly discussed. Also, many historical remarks are sprinkled throughout the book, and a biography of Lucas is included as an appendix.Much of the book is not intended to be overly detailed. Rather, the objective is to provide a good, elementary and clear explanation of the subject matter without too much ancillary material. Most chapters, with the exception of the second and the fourth, will address a particular theme, provide enough information for the reader to get a feel for the subject and supply references to more comprehensive results. Most of this work should be accessible to anyone with a basic knowledge of elementary number theory and abstract algebra. The book’s intended audience is number theorists, both professional and amateur, students and enthusiasts.

Index To Mathematical Problems 1980 1984

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Author : Stanley Rabinowitz
language : en
Publisher: MathPro Press
Release Date : 1992

Index To Mathematical Problems 1980 1984 written by Stanley Rabinowitz and has been published by MathPro Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992 with Mathematics categories.

A compendium of over 5,000 problems with subject, keyword, author and citation indexes.

Pell And Pell Lucas Numbers With Applications

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Author : Thomas Koshy
language : en
Publisher: Springer
Release Date : 2014-11-11

Pell And Pell Lucas Numbers With Applications written by Thomas Koshy and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-11-11 with Mathematics categories.

Pell and Pell–Lucas numbers, like the well-known Fibonacci and Catalan numbers, continue to intrigue the mathematical world with their beauty and applicability. They offer opportunities for experimentation, exploration, conjecture, and problem-solving techniques, connecting the fields of analysis, geometry, trigonometry, and various areas of discrete mathematics, number theory, graph theory, linear algebra, and combinatorics. Pell and Pell–Lucas numbers belong to an extended Fibonacci family as a powerful tool for extracting numerous interesting properties of a vast array of number sequences. A key feature of this work is the historical flavor that is interwoven into the extensive and in-depth coverage of the subject. An interesting array of applications to combinatorics, graph theory, geometry, and intriguing mathematical puzzles is another highlight engaging the reader. The exposition is user-friendly, yet rigorous, so that a broad audience consisting of students, math teachers and instructors, computer scientists and other professionals, along with the mathematically curious will all benefit from this book. Finally, Pell and Pell–Lucas Numbers provides enjoyment and excitement while sharpening the reader’s mathematical skills involving pattern recognition, proof-and-problem-solving techniques.

Algebraic Number Theoretic And Topological Aspects Of Ring Theory

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Author : Jean-Luc Chabert
language : en
Publisher: Springer Nature
Release Date : 2023-07-07

Algebraic Number Theoretic And Topological Aspects Of Ring Theory written by Jean-Luc Chabert and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-07-07 with Mathematics categories.

This volume has been curated from two sources: presentations from the Conference on Rings and Polynomials, Technische Universität Graz, Graz, Austria, July 19 –24, 2021, and papers intended for presentation at the Fourth International Meeting on Integer-valued Polynomials and Related Topics, CIRM, Luminy, France, which was cancelled due to the pandemic. The collection ranges widely over the algebraic, number theoretic and topological aspects of rings, algebras and polynomials. Two areas of particular note are topological methods in ring theory, and integer valued polynomials. The book is dedicated to the memory of Paul-Jean Cahen, a coauthor or research collaborator with some of the conference participants and a friend to many of the others. This collection contains a memorial article about Paul-Jean Cahen, written by his longtime research collaborator and coauthor Jean-Luc Chabert.

Catalan Numbers With Applications

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Author : Thomas Koshy
language : en
Publisher: OUP USA
Release Date : 2009

Catalan Numbers With Applications written by Thomas Koshy and has been published by OUP USA this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009 with Mathematics categories.

This book presents a clear and comprehensive introduction to one of the truly fascinating topics in mathematics: Catalan numbers. They crop up in chess, computer programming and even train tracks. In addition to lucid descriptions of the mathematics and history behind Catalan numbers, Koshy includes short biographies of the prominent mathematicians who have worked with the numbers.

Pell And Pell Lucas Numbers With Applications

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Author : Thomas Koshy
language : en
Publisher: Springer
Release Date : 2016-09-10

Fibonacci And Lucas Numbers With Applications Volume 2

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Author : Thomas Koshy
language : en
Publisher: John Wiley & Sons
Release Date : 2018-12-14

Fibonacci And Lucas Numbers With Applications Volume 2 written by Thomas Koshy and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-12-14 with Mathematics categories.

Volume II provides an advanced approach to the extended gibonacci family, which includes Fibonacci, Lucas, Pell, Pell-Lucas, Jacobsthal, Jacobsthal-Lucas, Vieta, Vieta-Lucas, and Chebyshev polynomials of both kinds. This volume offers a uniquely unified, extensive, and historical approach that will appeal to both students and professional mathematicians. As in Volume I, Volume II focuses on problem-solving techniques such as pattern recognition; conjecturing; proof-techniques, and applications. It offers a wealth of delightful opportunities to explore and experiment, as well as plentiful material for group discussions, seminars, presentations, and collaboration. In addition, the material covered in this book promotes intellectual curiosity, creativity, and ingenuity. Volume II features: A wealth of examples, applications, and exercises of varying degrees of difficulty and sophistication. Numerous combinatorial and graph-theoretic proofs and techniques. A uniquely thorough discussion of gibonacci subfamilies, and the fascinating relationships that link them. Examples of the beauty, power, and ubiquity of the extended gibonacci family. An introduction to tribonacci polynomials and numbers, and their combinatorial and graph-theoretic models. Abbreviated solutions provided for all odd-numbered exercises. Extensive references for further study. This volume will be a valuable resource for upper-level undergraduates and graduate students, as well as for independent study projects, undergraduate and graduate theses. It is the most comprehensive work available, a welcome addition for gibonacci enthusiasts in computer science, electrical engineering, and physics, as well as for creative and curious amateurs.

Current Trends In Symmetric Polynomials With Their Applications

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Author : Taekyun Kim
language : en
Publisher: MDPI
Release Date : 2019-10-15

Current Trends In Symmetric Polynomials With Their Applications written by Taekyun Kim and has been published by MDPI this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-10-15 with Mathematics categories.

This Special Issue presents research papers on various topics within many different branches of mathematics, applied mathematics, and mathematical physics. Each paper presents mathematical theories, methods, and their application based on current and recently developed symmetric polynomials. Also, each one aims to provide the full understanding of current research problems, theories, and applications on the chosen topics and includes the most recent advances made in the area of symmetric functions and polynomials.

Multiplicative Ideal Theory And Factorization Theory

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Author : Scott Chapman
language : en
Publisher: Springer
Release Date : 2016-07-29

Multiplicative Ideal Theory And Factorization Theory written by Scott Chapman and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-07-29 with Mathematics categories.

This book consists of both expository and research articles solicited from speakers at the conference entitled "Arithmetic and Ideal Theory of Rings and Semigroups," held September 22–26, 2014 at the University of Graz, Graz, Austria. It reflects recent trends in multiplicative ideal theory and factorization theory, and brings together for the first time in one volume both commutative and non-commutative perspectives on these areas, which have their roots in number theory, commutative algebra, and algebraic geometry. Topics discussed include topological aspects in ring theory, Prüfer domains of integer-valued polynomials and their monadic submonoids, and semigroup algebras. It will be of interest to practitioners of mathematics and computer science, and researchers in multiplicative ideal theory, factorization theory, number theory, and algebraic geometry.

The Integer Valued Polynomials On Lucas Numbers

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