Diophantine Equations And Systems

Author : Andrzej Tarlecki
Publisher : Springer Science & Business Media
Page : 458 pages
File Size : 47,6 Mb
Release : 1991-08-07
Category : Computers
ISBN : 3540543457

Get Book

Mathematical Foundations of Computer Science 1991 by Andrzej Tarlecki Pdf

This volume contains the proceedings of the 16th International Symposium on Mathematical Foundations of Computer Science, MFCS '91, held in Kazimierz Dolny, Poland, September 9-13, 1991. The series of MFCS symposia, organized alternately in Poland and Czechoslovakia since 1972, has a long and well established tradition. The purpose of the series is to encourage high-quality research in all branches of theoretical computer science and to bring together specialists working actively in the area. Principal areas of interest in this symposium include: software specification and development, parallel and distributed computing, logic and semantics of programs, algorithms, automata and formal languages, complexity and computability theory, and others. The volume contains 5 invited papers by distinguished scientists and 38 contributions selected from a total of 109 submitted papers.

Author : Titu Andreescu,Dorin Andrica,Ion Cucurezeanu
Publisher : Springer Science & Business Media
Page : 350 pages
File Size : 50,8 Mb
Release : 2010-09-02
Category : Mathematics
ISBN : 9780817645496

Get Book

An Introduction to Diophantine Equations by Titu Andreescu,Dorin Andrica,Ion Cucurezeanu Pdf

This problem-solving book is an introduction to the study of Diophantine equations, a class of equations in which only integer solutions are allowed. The presentation features some classical Diophantine equations, including linear, Pythagorean, and some higher degree equations, as well as exponential Diophantine equations. Many of the selected exercises and problems are original or are presented with original solutions. An Introduction to Diophantine Equations: A Problem-Based Approach is intended for undergraduates, advanced high school students and teachers, mathematical contest participants — including Olympiad and Putnam competitors — as well as readers interested in essential mathematics. The work uniquely presents unconventional and non-routine examples, ideas, and techniques.

Author : Alexander Schrijver
Publisher : John Wiley & Sons
Page : 488 pages
File Size : 51,8 Mb
Release : 1998-06-11
Category : Mathematics
ISBN : 0471982326

Get Book

Theory of Linear and Integer Programming by Alexander Schrijver Pdf

Als Ergänzung zu den mehr praxisorientierten Büchern, die auf dem Gebiet der linearen und Integerprogrammierung bereits erschienen sind, beschreibt dieses Werk die zugrunde liegende Theorie und gibt einen Überblick über wichtige Algorithmen. Der Autor diskutiert auch Anwendungen auf die kombinatorische Optimierung; neben einer ausführlichen Bibliographie finden sich umfangreiche historische Anmerkungen.

Author : Demetrios P Kanoussis Ph D
Publisher : Independently Published
Page : 0 pages
File Size : 47,9 Mb
Release : 2024-03-08
Category : Mathematics
ISBN : 9798884186637

Get Book

Diophantine Equations and Systems by Demetrios P Kanoussis Ph D Pdf

Diophantine equations are polynomial equations with integer coefficients for which only integer solutions are sought. In his great work "Arithmetica", the Greek mathematician Diophantus of Alexandria, (born in Alexandria Egypt in 200 AD and died in 284 AD), known as the father of Algebra, studied and solved such types of equations, (integer coefficients and integer solutions), of the first up to the fourth degree. These equations are now known as "Diophantine equations". A characteristic feature of Diophantine equations is that in these equations the number of equations is smaller than the number of unknowns. For example, we may have one equation with two unknowns, or one equation with three unknowns, or a system of two equations with three unknowns, etc. While in the set of real numbers R these types of equations, (fewer equations than number of unknowns), are indeterminate, in the set of integers Z={... -3, -2, -1,0,1,2,3, ...} or in the set of natural numbers N={1,2,3,4, ...}, these equations may or may not have integer solutions, (depending on the coefficients of the equations). In this book we provide a systematic introduction to Diophantine equations, with emphasis on the solution of various problems. The first two chapters are devoted to first degree Diophantine equations and systems, (linear equations and systems), while the third chapter is devoted to second degree Diophantine equations and systems. Among other equations, in this chapter, we study the Pythagorean equation (x^2+y^2=z^2), and the Pell's equation (x^2-ky^2=1). The solution of Pell's equation is achieved by a really brilliant method, which is attributed to Lagrange. Various examples of higher degree Diophantine equations are considered in chapter 4. The analytic description of the material covered in this book can be found in the table of contents. The book is concluded with a collection of 40 miscellaneous, challenging problems, with answers and detailed remarks and hints. In total, the book contains 55 solved examples and 105 problems for solution.

Author : Henri Cohen
Publisher : Springer Science & Business Media
Page : 673 pages
File Size : 50,8 Mb
Release : 2007-05-23
Category : Mathematics
ISBN : 9780387499222

Get Book

Number Theory by Henri Cohen Pdf

The central theme of this book is the solution of Diophantine equations, i.e., equations or systems of polynomial equations which must be solved in integers, rational numbers or more generally in algebraic numbers. This theme, in particular, is the central motivation for the modern theory of arithmetic algebraic geometry. In this text, this is considered through three of its most basic aspects. The book contains more than 350 exercises and the text is largely self-contained. Much more sophisticated techniques have been brought to bear on the subject of Diophantine equations, and for this reason, the author has included five appendices on these techniques.

Author : Yuan Wang
Publisher : Springer Science & Business Media
Page : 185 pages
File Size : 49,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642581717

Get Book

Diophantine Equations and Inequalities in Algebraic Number Fields by Yuan Wang Pdf

The circle method has its genesis in a paper of Hardy and Ramanujan (see [Hardy 1])in 1918concernedwiththepartitionfunction andtheproblemofrep resenting numbers as sums ofsquares. Later, in a series of papers beginning in 1920entitled "some problems of'partitio numerorum''', Hardy and Littlewood (see [Hardy 1]) created and developed systematically a new analytic method, the circle method in additive number theory. The most famous problems in ad ditive number theory, namely Waring's problem and Goldbach's problem, are treated in their papers. The circle method is also called the Hardy-Littlewood method. Waring's problem may be described as follows: For every integer k 2 2, there is a number s= s(k) such that every positive integer N is representable as (1) where Xi arenon-negative integers. This assertion wasfirst proved by Hilbert [1] in 1909. Using their powerful circle method, Hardy and Littlewood obtained a deeper result on Waring's problem. They established an asymptotic formula for rs(N), the number of representations of N in the form (1), namely k 1 provided that 8 2 (k - 2)2 - +5. Here

Author : Henri Cohen
Publisher : Springer Science & Business Media
Page : 673 pages
File Size : 47,8 Mb
Release : 2008-10-10
Category : Mathematics
ISBN : 9780387499239

Get Book

Number Theory by Henri Cohen Pdf

The central theme of this book is the solution of Diophantine equations, i.e., equations or systems of polynomial equations which must be solved in integers, rational numbers or more generally in algebraic numbers. This theme, in particular, is the central motivation for the modern theory of arithmetic algebraic geometry. In this text, this is considered through three of its most basic aspects. The book contains more than 350 exercises and the text is largely self-contained. Much more sophisticated techniques have been brought to bear on the subject of Diophantine equations, and for this reason, the author has included five appendices on these techniques.

Author : Joseph Tsu-wu Chou
Publisher : Unknown
Page : 264 pages
File Size : 51,9 Mb
Release : 1979
Category : Diophantine analysis
ISBN : WISC:89011026028

Get Book

Algorithms for the Solution of Systems of Linear Diophantine Equations by Joseph Tsu-wu Chou Pdf

Author : Panos J. Antsaklis,Anthony N. Michel
Publisher : Springer Science & Business Media
Page : 672 pages
File Size : 44,8 Mb
Release : 2006-11-24
Category : Technology & Engineering
ISBN : 9780817644352

Get Book

Linear Systems by Panos J. Antsaklis,Anthony N. Michel Pdf

"There are three words that characterize this work: thoroughness, completeness and clarity. The authors are congratulated for taking the time to write an excellent linear systems textbook!" —IEEE Transactions on Automatic Control Linear systems theory plays a broad and fundamental role in electrical, mechanical, chemical and aerospace engineering, communications, and signal processing. A thorough introduction to systems theory with emphasis on control is presented in this self-contained textbook, written for a challenging one-semester graduate course. A solutions manual is available to instructors upon adoption of the text. The book’s flexible coverage and self-contained presentation also make it an excellent reference guide or self-study manual. For a treatment of linear systems that focuses primarily on the time-invariant case using streamlined presentation of the material with less formal and more intuitive proofs, please see the authors’ companion book entitled A Linear Systems Primer.

Author : Octavian Cira,Florentin Smarandache
Publisher : Infinite Study
Page : 128 pages
File Size : 51,6 Mb
Release : 2024-06-29
Category : Electronic
ISBN : 9781599733074

Get Book

Solving Diophantine Equations by Octavian Cira,Florentin Smarandache Pdf

In this book a multitude of Diophantine equations and their partial or complete solutions are presented. How should we solve, for example, the equation η(π(x)) = π(η(x)), where η is the Smarandache function and π is Riemann function of counting the number of primes up to x, in the set of natural numbers? If an analytical method is not available, an idea would be to recall the empirical search for solutions. We establish a domain of searching for the solutions and then we check all possible situations, and of course we retain among them only those solutions that verify our equation. In other words, we say that the equation does not have solutions in the search domain, or the equation has n solutions in this domain. This mode of solving is called partial resolution. Partially solving a Diophantine equation may be a good start for a complete solving of the problem. The authors have identified 62 Diophantine equations that impose such approach and they partially solved them. For an efficient resolution it was necessarily that they have constructed many useful ”tools” for partially solving the Diophantine equations into a reasonable time. The computer programs as tools were written in Mathcad, because this is a good mathematical software where many mathematical functions are implemented. Transposing the programs into another computer language is facile, and such algorithms can be turned to account on other calculation systems with various processors.

Author : John Owen Ethridge
Publisher : Unknown
Page : 112 pages
File Size : 52,9 Mb
Release : 1950
Category : Diophantine analysis
ISBN : UGA:32108002447483

Get Book

A Study of Linear Diophantine Equations and Systems of Linear Diophantine Equations by John Owen Ethridge Pdf

Author : Hasan Sankari,Mohammad Abobala
Publisher : Infinite Study
Page : 10 pages
File Size : 43,6 Mb
Release : 2020-12-01
Category : Mathematics
ISBN : 8210379456XXX

Get Book

Neutrosophic Linear Diophantine Equations With Two Variables by Hasan Sankari,Mohammad Abobala Pdf

This paper is devoted to study for the first time the neutrosophic linear Diophantine equations with two variables in the neutrosophic ring of integers, and refined neutrosophic ring of integers. This work introduces an algorithm to solve the linear Diophantine equation.

Author : Anonim
Publisher : Academic Press
Page : 311 pages
File Size : 55,5 Mb
Release : 1969
Category : Mathematics
ISBN : 0080873421

Get Book

Diophantine Equations by Anonim Pdf

Diophantine Equations

Author : Henri Cohen
Publisher : Springer
Page : 0 pages
File Size : 41,6 Mb
Release : 2007-05-23
Category : Mathematics
ISBN : 0387499229

Get Book

Number Theory by Henri Cohen Pdf

The central theme of this book is the solution of Diophantine equations, i.e., equations or systems of polynomial equations which must be solved in integers, rational numbers or more generally in algebraic numbers. This theme, in particular, is the central motivation for the modern theory of arithmetic algebraic geometry. In this text, this is considered through three of its most basic aspects. The book contains more than 350 exercises and the text is largely self-contained. Much more sophisticated techniques have been brought to bear on the subject of Diophantine equations, and for this reason, the author has included five appendices on these techniques.

Author : Florentin Smarandache
Publisher : Infinite Study
Page : 9 pages
File Size : 50,6 Mb
Release : 2024-06-29
Category : Electronic
ISBN : 8210379456XXX

Get Book

ALGORITHMS FOR SOLVING LINEAR CONGRUENCES AND SYSTEMS OF LINEAR CONGRUENCES by Florentin Smarandache Pdf

In this article we determine several theorems and methods for solving linear congruences and systems of linear congruences and we find the number of distinct solutions. Many examples of solving congruences are given.