Download or read book Diophantus and Diophantine Equations written by Izabella Grigorʹevna Bashmakova and published by Cambridge University Press. This book was released on 1997 with total page 110 pages. Available in PDF, EPUB and Kindle. Book excerpt: Semi-popular maths on an area of number theory related to Fermat.
Download or read book Diophantus and Diophantine Equations written by Isabella Grigoryevna Bashmakova and published by American Mathematical Soc.. This book was released on 2019-01-29 with total page 90 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book tells the story of Diophantine analysis, a subject that, owing to its thematic proximity to algebraic geometry, became fashionable in the last half century and has remained so ever since. This new treatment of the methods of Diophantus--a person whose very existence has long been doubted by most historians of mathematics--will be accessible to readers who have taken some university mathematics. It includes the elementary facts of algebraic geometry indispensable for its understanding. The heart of the book is a fascinating account of the development of Diophantine methods during the.
Download or read book An Introduction to Diophantine Equations written by Titu Andreescu and published by Springer Science & Business Media. This book was released on 2010-09-02 with total page 350 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Quadratic Diophantine Equations written by Titu Andreescu and published by Springer. This book was released on 2015-06-29 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text treats the classical theory of quadratic diophantine equations and guides the reader through the last two decades of computational techniques and progress in the area. The presentation features two basic methods to investigate and motivate the study of quadratic diophantine equations: the theories of continued fractions and quadratic fields. It also discusses Pell’s equation and its generalizations, and presents some important quadratic diophantine equations and applications. The inclusion of examples makes this book useful for both research and classroom settings.
Download or read book Diophantus and Diophantine Equations written by Isabella Grigoryevna Bashmakova and published by American Mathematical Soc.. This book was released on 2019-01-18 with total page 90 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book tells the story of Diophantine analysis, a subject that, owing to its thematic proximity to algebraic geometry, became fashionable in the last half century and has remained so ever since. This new treatment of the methods of Diophantus—a person whose very existence has long been doubted by most historians of mathematics—will be accessible to readers who have taken some university mathematics. It includes the elementary facts of algebraic geometry indispensable for its understanding. The heart of the book is a fascinating account of the development of Diophantine methods during the Renaissance and in the work of Fermat. This account is continued to our own day and ends with an afterword by Joseph Silverman, who notes the most recent developments including the proof of Fermat's Last Theorem.
Download or read book Diophantine Approximations and Diophantine Equations written by Wolfgang M. Schmidt and published by Springer. This book was released on 2006-12-08 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt: "This book by a leading researcher and masterly expositor of the subject studies diophantine approximations to algebraic numbers and their applications to diophantine equations. The methods are classical, and the results stressed can be obtained without much background in algebraic geometry. In particular, Thue equations, norm form equations and S-unit equations, with emphasis on recent explicit bounds on the number of solutions, are included. The book will be useful for graduate students and researchers." (L'Enseignement Mathematique) "The rich Bibliography includes more than hundred references. The book is easy to read, it may be a useful piece of reading not only for experts but for students as well." Acta Scientiarum Mathematicarum
Download or read book Diophantus And Arithmetica written by Dr. Arun Kumar Mishra and published by Booksclinic Publishing. This book was released on 2022-12-13 with total page 138 pages. Available in PDF, EPUB and Kindle. Book excerpt: ‘Arithmetica’ is an eminent book of mathematics, written by a Greek mathematician Diophantus. A systematic work on Diophantus was performed by Sir Thomas L. Heath, K.C.B. Sir Thomas L. Heath had written a very impressive book entitled, “Diophantus of Alexandria: A study in the History of Greek Algebra”. The first edition of the book in English on Diophantus appeared in 1885.
Download or read book Diophantine Equations and Systems written by Demetrios P Kanoussis Ph D and published by Independently Published. This book was released on 2024-03-08 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Solving Diophantine Equations written by Octavian Cira and published by Infinite Study. This book was released on 2014 with total page 254 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Diophantine Equations written by and published by Academic Press. This book was released on 1969 with total page 327 pages. Available in PDF, EPUB and Kindle. Book excerpt: Diophantine Equations
Download or read book Unit Equations in Diophantine Number Theory written by Jan-Hendrik Evertse and published by Cambridge University Press. This book was released on 2015-12-30 with total page 381 pages. Available in PDF, EPUB and Kindle. Book excerpt: A comprehensive, graduate-level treatment of unit equations and their various applications.
Download or read book Lecture Notes on Diophantine Analysis written by Umberto Zannier and published by Springer. This book was released on 2015-05-05 with total page 248 pages. Available in PDF, EPUB and Kindle. Book excerpt: These lecture notes originate from a course delivered at the Scuola Normale in Pisa in 2006. Generally speaking, the prerequisites do not go beyond basic mathematical material and are accessible to many undergraduates. The contents mainly concern diophantine problems on affine curves, in practice describing the integer solutions of equations in two variables. This case historically suggested some major ideas for more general problems. Starting with linear and quadratic equations, the important connections with Diophantine Approximation are presented and Thue's celebrated results are proved in full detail. In later chapters more modern issues on heights of algebraic points are dealt with, and applied to a sharp quantitative treatment of the unit equation. The book also contains several supplements, hinted exercises and an appendix on recent work on heights.
Download or read book Diophantine Analysis 1915 written by Robert Daniel Carmichael and published by . This book was released on 2008-08-01 with total page 128 pages. Available in PDF, EPUB and Kindle. Book excerpt: This scarce antiquarian book is a facsimile reprint of the original. Due to its age, it may contain imperfections such as marks, notations, marginalia and flawed pages. Because we believe this work is culturally important, we have made it available as part of our commitment for protecting, preserving, and promoting the world's literature in affordable, high quality, modern editions that are true to the original work.
Download or read book Classical Diophantine Equations written by Vladimir Gennadievich Sprindzhuk and published by Springer. This book was released on 1993 with total page 248 pages. Available in PDF, EPUB and Kindle. Book excerpt: The author had initiated a revision and translation of "Classical Diophantine Equations" prior to his death. Given the rapid advances in transcendence theory and diophantine approximation over recent years, one might fear that the present work, originally published in Russian in 1982, is mostly superseded. That is not so. A certain amount of updating had been prepared by the author himself before his untimely death. Some further revision was prepared by close colleagues. The first seven chapters provide a detailed, virtually exhaustive, discussion of the theory of lower bounds for linear forms in the logarithms of algebraic numbers and its applications to obtaining upper bounds for solutions to the eponymous classical diophantine equations. The detail may seem stark--- the author fears that the reader may react much as does the tourist on first seeing the centre Pompidou; notwithstanding that, Sprind zuk maintainsa pleasant and chatty approach, full of wise and interesting remarks. His emphases well warrant, now that the book appears in English, close studyand emulation. In particular those emphases allow him to devote the eighth chapter to an analysis of the interrelationship of the class number of algebraic number fields involved and the bounds on the heights of thesolutions of the diophantine equations. Those ideas warrant further development. The final chapter deals with effective aspects of the Hilbert Irreducibility Theorem, harkening back to earlier work of the author. There is no other congenial entry point to the ideas of the last two chapters in the literature.
Download or read book Diophantine m tuples and Elliptic Curves written by Andrej Dujella and published by Springer Nature. This book was released on with total page 343 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book On some properties of the Diophantine equations written by Abdullah-Al-Kafi Majumdar and published by Infinite Study. This book was released on with total page 4 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper gives some properties related to the Diophantine equations a2 = b2 ± bc +c2. It has been shown that, in some cases, each of the two Diophantine equations has multiple solutions. The formulas for multiple solutions are derived.
Download or read book Diophantus of Alexandria A Study in the History of Greek Algebra written by Thomas Little Heath and published by Franklin Classics Trade Press. This book was released on 2018-11-08 with total page 398 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work has been selected by scholars as being culturally important and is part of the knowledge base of civilization as we know it. This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. To ensure a quality reading experience, this work has been proofread and republished using a format that seamlessly blends the original graphical elements with text in an easy-to-read typeface. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
