A Troupe Of Special Second Degree Multivariable Polynomial Diophantine Equations With Integer Solutions
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A Troupe Of Special Second Degree Multivariable Polynomial Diophantine Equations With Integer Solutions
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Author : M. A. Gopalan
language : en
Publisher: Deep Science Publishing
Release Date : 2025-01-24
A Troupe Of Special Second Degree Multivariable Polynomial Diophantine Equations With Integer Solutions written by M. A. Gopalan and has been published by Deep Science Publishing this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-01-24 with Mathematics categories.
The fascinating branch of Mathematics is the Theory of Numbers in which the subject of Diophantine equations requiring only the integer solutions is an interesting area to various mathematicians and to the lovers of mathematics because it is a treasure house in which the search for many hidden connections is a treasure hunt. In other words, the theory of Diophantine equations is an ancient subject that typically involves solving, polynomial equation in two or more variables or a system of polynomial equations with the number of unknowns greater than the number of equations, in integers and occupies a pivotal role in the region of mathematics. It is worth to mention that the Diophantine problems are plenty playing a significant role in the development of mathematics because the beauty of Diophantine equations is that the number of equations is less than the number of unknowns. The theory of Diophantine equations provides a fertile ground for both professionals and amateurs. In addition to known results, the theory of Diophantine equations abounds with unsolved problems (Carmichael.,1959; Dickson.,1952; Mordell.,1969). In this context, for simplicity and brevity, one may refer Gopalan et.al., 2012, 2015, 2021, 2024; Mahalakshmi, Shanthi., 2023; Sathiyapriya et.al., 2024; Shanthi.,2023; Shanthi, Mahalakshmi.,2023; Shanthi, Gopalan.,2024; Thiruniraiselvi, Gopalan., 2024; Vidhyalakshmi et.al., 2022 for some binary and ternary quadratic Diophantine equations. Although many of its results can be stated in simple and elegant terms, their proofs are sometimes long and complicated. Many unsolved problems that have been daunting mathematicians for centuries provide unlimited opportunities to expand the frontiers of mathematical knowledge. The subject of Diophantine equations has fascinated and inspired both amateurs and mathematicians alike and so they merit special recognition. The successful completion of exhibiting all integers satisfying the requirements set forth in the problem add to further progress of Number Theory as they offer good applications in the field of Graph theory, Modular theory, Coding and Cryptography, Engineering, Music and so on. Integers have repeatedly played a crucial role in the evolution of the Natural Sciences. The theory of integers provides answers to real world problems. The focus in this book is on solving multivariable second-degree Diophantine equations. These types of equations can be challenging as they involve finding integer solutions that satisfy the given polynomial equation. Learning about the various techniques to solve these multivariable second-degree Diophantine equations in successfully deriving their solutions help us understand how numbers work and their significance in different areas of mathematics and science. This book contains a reasonable collection of special multivariable Quadratic Diophantine problems in three, four and five variables. The process of getting different sets of integer solutions to each of the quadratic Diophantine equations considered in this book are illustrated in an elegant manner.
Undergraduate Announcement
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Author : University of Michigan--Dearborn
language : en
Publisher:
Release Date : 1989
Undergraduate Announcement written by University of Michigan--Dearborn and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989 with categories.
Applications Of Fibonacci Numbers
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Author : G.E. Bergum
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Applications Of Fibonacci Numbers written by G.E. Bergum and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
This book contains 43 papers form among the 55 papers presented at the Sixth International Conference on Fibonacci Numbers and Their Applications which was held at Washington State University, Pullman, Washington, from July 18-22, 1994. These papers have been selected after a careful review by well known referees in the field, and they range from elementary number theory to probability and statistics. The Fibonacci numbers and recurrence relations are their unifying bond. It is anticipated that this book, like its five predecessors, will be useful to research workers and graduate students interested in the Fibonacci numbers and their applications. October 30, 1995 The Editors Gerald E. Bergum South Dakota State University Brookings, South Dakota, U.S.A. Alwyn F. Horadam University of New England Armidale, N.S.W., Australia Andreas N. Philippou 26 Atlantis Street Aglangia, Nicosia Cyprus xxi THE ORGANIZING COMMITTEES LOCAL COMMITTEE INTERNATIONAL COMMITTEE Long, Calvin T., Co-Chair Horadam, A.F. (Australia), Co-Chair Webb, William A., Co-Chair Philippou, A.N. (Cyprus), Co-Chair Burke, John Ando, S. (Japan) DeTemple, Duane W.
Exponential Diophantine Equations
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Author : T. N. Shorey
language : en
Publisher: Cambridge University Press
Release Date : 1986-11-27
Exponential Diophantine Equations written by T. N. Shorey and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1986-11-27 with Mathematics categories.
This is a integrated presentation of the theory of exponential diophantine equations. The authors present, in a clear and unified fashion, applications to exponential diophantine equations and linear recurrence sequences of the Gelfond-Baker theory of linear forms in logarithms of algebraic numbers. Topics covered include the Thue equations, the generalised hyperelliptic equation, and the Fermat and Catalan equations. The necessary preliminaries are given in the first three chapters. Each chapter ends with a section giving details of related results.
Mathematical Reviews
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Author :
language : en
Publisher:
Release Date : 2004
Mathematical Reviews written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Mathematics categories.
Putnam And Beyond
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Author : Razvan Gelca
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-08-11
Putnam And Beyond written by Razvan Gelca and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-08-11 with Mathematics categories.
Putnam and Beyond takes the reader on a journey through the world of college mathematics, focusing on some of the most important concepts and results in the theories of polynomials, linear algebra, real analysis in one and several variables, differential equations, coordinate geometry, trigonometry, elementary number theory, combinatorics, and probability. Using the W.L. Putnam Mathematical Competition for undergraduates as an inspiring symbol to build an appropriate math background for graduate studies in pure or applied mathematics, the reader is eased into transitioning from problem-solving at the high school level to the university and beyond, that is, to mathematical research.
Encyclopaedia Of Mathematics
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Author : Michiel Hazewinkel
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Encyclopaedia Of Mathematics written by Michiel Hazewinkel and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
This is the second supplementary volume to Kluwer's highly acclaimed eleven-volume Encyclopaedia of Mathematics. This additional volume contains nearly 500 new entries written by experts and covers developments and topics not included in the previous volumes. These entries are arranged alphabetically throughout and a detailed index is included. This supplementary volume enhances the existing eleven volumes, and together these twelve volumes represent the most authoritative, comprehensive and up-to-date Encyclopaedia of Mathematics available.
Solving Systems Of Polynomial Equations
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Author : Bernd Sturmfels
language : en
Publisher: American Mathematical Soc.
Release Date : 2002
Solving Systems Of Polynomial Equations written by Bernd Sturmfels and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002 with Mathematics categories.
Bridging a number of mathematical disciplines, and exposing many facets of systems of polynomial equations, Bernd Sturmfels's study covers a wide spectrum of mathematical techniques and algorithms, both symbolic and numerical.
Problems In Algebraic Number Theory
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Author : M. Ram Murty
language : en
Publisher: Springer Science & Business Media
Release Date : 2005
Problems In Algebraic Number Theory written by M. Ram Murty and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with Mathematics categories.
The problems are systematically arranged to reveal the evolution of concepts and ideas of the subject Includes various levels of problems - some are easy and straightforward, while others are more challenging All problems are elegantly solved
The Algorithmic Resolution Of Diophantine Equations
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Author : Nigel P. Smart
language : en
Publisher: Cambridge University Press
Release Date : 1998-11-12
The Algorithmic Resolution Of Diophantine Equations written by Nigel P. Smart and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-11-12 with Mathematics categories.
A coherent account of the computational methods used to solve diophantine equations.