Download or read book Geometric Theorems Diophantine Equations and Arithmetic Functions written by J. Sándor and published by Infinite Study. This book was released on 2002 with total page 302 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Geometric Theorems Diophantine Equations and Arithmetic Functions written by J. Sándor and published by . This book was released on 2014-05-14 with total page 302 pages. Available in PDF, EPUB and Kindle. Book excerpt: Made available online by the Smarandache Notion Journal and the University of New Mexico - Gallup.

Download or read book Geometric Theorems and Arithmetic Functions written by József Sándor and published by Infinite Study. This book was released on 2002 with total page 55 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Various Arithmetic Functions and their Applications written by Octavian Cira and published by Infinite Study. This book was released on 2016 with total page 402 pages. Available in PDF, EPUB and Kindle. Book excerpt: Over 300 sequences and many unsolved problems and conjectures related to them are presented herein. These notions, definitions, unsolved problems, questions, theorems corollaries, formulae, conjectures, examples, mathematical criteria, etc. on integer sequences, numbers, quotients, residues, exponents, sieves, pseudo-primes squares cubes factorials, almost primes, mobile periodicals, functions, tables, prime square factorial bases, generalized factorials, generalized palindromes, so on, have been extracted from the Archives of American Mathematics (University of Texas at Austin) and Arizona State University (Tempe): "The Florentin Smarandache papers" special collections, and Arhivele Statului (Filiala Vâlcea & Filiala Dolj, Romania). This book was born from the collaboration of the two authors, which started in 2013. The first common work was the volume "Solving Diophantine Equations", published in 2014. The contribution of the authors can be summarized as follows: Florentin Smarandache came with his extraordinary ability to propose new areas of study in number theory, and Octavian Cira - with his algorithmic thinking and knowledge of Mathcad.

Download or read book The Queen of Mathematics written by W.S. Anglin and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 393 pages. Available in PDF, EPUB and Kindle. Book excerpt: Like other introductions to number theory, this one includes the usual curtsy to divisibility theory, the bow to congruence, and the little chat with quadratic reciprocity. It also includes proofs of results such as Lagrange's Four Square Theorem, the theorem behind Lucas's test for perfect numbers, the theorem that a regular n-gon is constructible just in case phi(n) is a power of 2, the fact that the circle cannot be squared, Dirichlet's theorem on primes in arithmetic progressions, the Prime Number Theorem, and Rademacher's partition theorem. We have made the proofs of these theorems as elementary as possible. Unique to The Queen of Mathematics are its presentations of the topic of palindromic simple continued fractions, an elementary solution of Lucas's square pyramid problem, Baker's solution for simultaneous Fermat equations, an elementary proof of Fermat's polygonal number conjecture, and the Lambek-Moser-Wild theorem.

Download or read book The Math Encyclopedia of Smarandache type Notions written by Marius Coman and published by Infinite Study. This book was released on with total page 136 pages. Available in PDF, EPUB and Kindle. Book excerpt: About the works of Florentin Smarandache have been written a lot of books (he himself wrote dozens of books and articles regarding math, physics, literature, philosophy). Being a globally recognized personality in both mathematics (there are countless functions and concepts that bear his name) and literature, it is natural that the volume of writings about his research is huge. What we try to do with this encyclopedia is to gather together as much as we can both from Smarandache’s mathematical work and the works of many mathematicians around the world inspired by the Smarandache notions. We structured this book using numbered Definitions, Theorems, Conjectures, Notes and Comments, in order to facilitate an easier reading but also to facilitate references to a specific paragraph. We divided the Bibliography in two parts, Writings by Florentin Smarandache (indexed by the name of books and articles) and Writings on Smarandache notions (indexed by the name of authors). We treated, in this book, about 130 Smarandache type sequences, about 50 Smarandache type functions and many solved or open problems of number theory. We also have, at the end of this book, a proposal for a new Smarandache type notion, id est the concept of “a set of Smarandache-Coman divisors of order k of a composite positive integer n with m prime factors”, notion that seems to have promising applications, at a first glance at least in the study of absolute and relative Fermat pseudoprimes, Carmichael numbers and Poulet numbers. This encyclopedia is both for researchers that will have on hand a tool that will help them “navigate” in the universe of Smarandache type notions and for young math enthusiasts: many of them will be attached by this wonderful branch of mathematics, number theory, reading the works of Florentin Smarandache.

Download or read book Diophantine Geometry written by Marc Hindry and published by Springer Science & Business Media. This book was released on 2013-12-01 with total page 574 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is an introduction to diophantine geometry at the advanced graduate level. The book contains a proof of the Mordell conjecture which will make it quite attractive to graduate students and professional mathematicians. In each part of the book, the reader will find numerous exercises.

Download or read book NOTES ON NUMBER THEORY AND DISCRETE MATHEMATICS VOLUME 9 NUMBER 2 2003 written by Aldo Peretti and published by Infinite Study. This book was released on with total page 12 pages. Available in PDF, EPUB and Kindle. Book excerpt: Articles, notes and problems on Smarandache Function, Pseudo-Smarandache function, Smarandache-simple functions, Inferior Smarandache Prime Part, Smarandache double factorial function, Generalized Smarandache Palindrome, Smarandache problems, Smarandache circular sequence etc.

Download or read book Handbook of Number Theory I written by József Sándor and published by Springer Science & Business Media. This book was released on 2005-11-17 with total page 638 pages. Available in PDF, EPUB and Kindle. Book excerpt: This handbook covers a wealth of topics from number theory, special attention being given to estimates and inequalities. As a rule, the most important results are presented, together with their refinements, extensions or generalisations. These may be applied to other aspects of number theory, or to a wide range of mathematical disciplines. Cross-references provide new insight into fundamental research. Audience: This is an indispensable reference work for specialists in number theory and other mathematicians who need access to some of these results in their own fields of research.

Download or read book Scalar Vector and Matrix Mathematics written by Dennis S. Bernstein and published by Princeton University Press. This book was released on 2018-02-27 with total page 1600 pages. Available in PDF, EPUB and Kindle. Book excerpt: The essential reference book on matrices—now fully updated and expanded, with new material on scalar and vector mathematics Since its initial publication, this book has become the essential reference for users of matrices in all branches of engineering, science, and applied mathematics. In this revised and expanded edition, Dennis Bernstein combines extensive material on scalar and vector mathematics with the latest results in matrix theory to make this the most comprehensive, current, and easy-to-use book on the subject. Each chapter describes relevant theoretical background followed by specialized results. Hundreds of identities, inequalities, and facts are stated clearly and rigorously, with cross-references, citations to the literature, and helpful comments. Beginning with preliminaries on sets, logic, relations, and functions, this unique compendium covers all the major topics in matrix theory, such as transformations and decompositions, polynomial matrices, generalized inverses, and norms. Additional topics include graphs, groups, convex functions, polynomials, and linear systems. The book also features a wealth of new material on scalar inequalities, geometry, combinatorics, series, integrals, and more. Now more comprehensive than ever, Scalar, Vector, and Matrix Mathematics includes a detailed list of symbols, a summary of notation and conventions, an extensive bibliography and author index with page references, and an exhaustive subject index. Fully updated and expanded with new material on scalar and vector mathematics Covers the latest results in matrix theory Provides a list of symbols and a summary of conventions for easy and precise use Includes an extensive bibliography with back-referencing plus an author index

Download or read book Wandering in the World of Smarandache Numbers written by A. A. K. Majumdar and published by Infinite Study. This book was released on 2010 with total page 217 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book covers only a part of the wide and diverse field of the Smarandache Notions, andcontains some of the materials that I gathered as I wandered in the world of Smarandache. Mostof the materials are already published in different journals, but some materials are new andappear for the first time in this book. All the results are provided with proofs._ Chapter 1 gives eleven recursive type Smarandache sequences, namely, the SmarandacheOdd, Even, Prime Product, Square Product (of two types), Higher Power Product (of twotypes), Permutation, Circular, Reverse, Symmetric and Pierced Chain sequences_ Chapter 2 deals with the Smarandache Cyclic Arithmetic Determinant and BisymmetricArithmetic Determinant sequences, and series involving the terms of the Smarandachebisymmetric determinant natural and bisymmetric arithmetic determinant sequences_ Chapter 3 treats the Smarandache function S(n)_ Chapter 4 considers, in rather more detail, the pseudo Smarandache function Z(n)_ And the Smarandache S-related and Z-related triangles are the subject matter of Chapter 5.To make the book self-contained, some well-known results of the classical Number Theory aregiven in Chapter 0. In order to make the book up-to-date, the major results of other researchersare also included in the book.At the end of each chapter, several open problems are given.

Download or read book Scientia Magna Vol 7 No 4 2011 written by Zhang Wenpeng and published by Infinite Study. This book was released on with total page 128 pages. Available in PDF, EPUB and Kindle. Book excerpt: Papers on Smarandache function S(n), Erdos-Smarandache numbers, generalized intuitionistic fuzzy contra continuous functions and its applications, the asymptotic properties of triangular base sequence, linear operators preserving commuting pairs of matrices over semirings, two inequalities for the composition of arithmetic functions, compactness and proper maps in the category of generated spaces, and similar topics. Contributors: R. Ma, Y. Zhang, R. Dhavaseelan, M. Dragan, M. Bencze, Q. Yang, G. Mirhosseinkhani, C. Fu, S. S. Billing, B. Hazarika, and others.

Download or read book Scientia Magna Vol 8 No 2 2012 written by Zhang Wenpeng and published by Infinite Study. This book was released on with total page 135 pages. Available in PDF, EPUB and Kindle. Book excerpt: Papers on Smarandache groupoids, a new class of generalized semiclosed sets using grills, Smarandache friendly numbers, a simple proof of the Sophie Germain primes problem along with the Mersenne primes problem and their connection to the Fermat's last conjecture, uniqueness of solutions of linear integral equations of the first kind with two variables, and similar topics. Contributors: A. A. Nithya, I. A. Rani, I. Arockiarani, V. Vinodhini, A. A. K. Majumdar, N. Subramanian, C. Murugesan, I. A. G. Nemron, S. I. Cenberci, B. Peker, P. Muralikrishna, M. Chandramouleeswaran, I. A. Rani, A. Karthika, and others.

Download or read book SMARANDACHE NUMBERS REVISITED written by A.A.K. MAJUMDAR and published by Infinite Study. This book was released on with total page 132 pages. Available in PDF, EPUB and Kindle. Book excerpt: More than seven years ago, my first book on some of the Smarandache notions was published. The book consisted of five chapters, and the topics covered were as follows : (1) some recursive type Smarandache sequences, (2) Smarandache determinant sequences, (3) the Smarandache function, (4) the pseudo Smarandache function, and (5) the Smarandache function related and the pseudo Smarandache function related triangles. Since then, new and diversified results have been published by different researchers. The aim of this book to update some of the contents of my previous book, and add some new results.

Download or read book Scientia Magna Vol 1 No 1 2005 written by Zhang Wenpeng and published by Infinite Study. This book was released on 2006-01-01 with total page 222 pages. Available in PDF, EPUB and Kindle. Book excerpt: Collection of papers from various scientists dealing with smarandache notions in science.

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 Scientia Magna Vol 6 No 2 2010 written by Zhang Wenpeng and published by Infinite Study. This book was released on with total page 139 pages. Available in PDF, EPUB and Kindle. Book excerpt: Papers on Smarandache's Orthic Theorem, Smarandache's Concurrent Lines Theorem, character graph in Brauer graph's model, robust stability of switched linear systems with time-varying delay, majority neighborhood number of a graph, divisibility tests for Smarandache semigroups, Hopf bifurcation in a predator-prey model with distributed delays, and similar topics. Contributors: R. S. Maragatham, S. Asawasamarit, U. Leerawat, S. Balasubramanian, D. Senthilkumar, M. Khoshnevisan, D. Senthilkumar, Sherinjoy S. M., and others.