Download or read book A survey on Smarandache notions in number theory VII Smarandache multiplicative function written by Yuchan Qi and published by Infinite Study. This book was released on with total page 9 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper we give a survey on recent results on Smarandache multiplicative function.
Download or read book A survey on Smarandache notions in number theory VI Smarandache Ceil function written by Xiaolin Chen and published by Infinite Study. This book was released on with total page 8 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper we give a survey on recent results on Smarandache Ceil function.
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 A survey on Smarandache notions in number theory II pseudo Smarandache function written by Huaning Liu and published by Infinite Study. This book was released on with total page 9 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper we give a survey on recent results on pseudo-Smarandache function.
Download or read book Some Results on the Sandor Smarandache Function written by S. M. S. Islam and published by Infinite Study. This book was released on with total page 12 pages. Available in PDF, EPUB and Kindle. Book excerpt: Sandor introduced a new Smarandache-type function, denoted by SS(n), and is called the Sandor-Smarandache function. When n is an odd (positive) integer, then SS(n) has a very simple form, as has been derived by Sandor himself. However, when n is even, then the form of SS(n) is not simple, and remains an open problem. This paper finds SS(n) for some special cases of n. Particular attention is given to values of the general forms SS(2mp), SS(6mp), SS(60mp) and SS(420mp), where m is any (positive) integer and p is an odd prime. Some particular cases have been treated in detail. In Section 4, some remarks are observed.
Download or read book A Set of New Smarandache Functions Sequences and Conjectures written by Felice Russo and published by Infinite Study. This book was released on 2000 with total page 108 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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 Smarandache Notions written by and published by . This book was released on 2004 with total page 422 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Smarandache Notions Vol 14 written by W. B. Vasantha Kandasamy and published by Infinite Study. This book was released on 2004-01-01 with total page 418 pages. Available in PDF, EPUB and Kindle. Book excerpt: Papers concerning any of the Smarandache type functions, sequences, numbers, algorithms, inferior/superior f-parts, magic squares, palindromes, functional iterations, semantic paradoxes, Non-Euclidean geometries, manifolds, conjectures, open problems, algebraic structures, neutrosophy, neutrosophic logic/set/probability, hypothesis that there is no speed barrier in the universe, quantum paradoxes, etc. have been selected for this volume. Contributors are from Australia, China, England, Germany, India, Ireland, Israel, Italy, Japan, Malaysia, Morocco, Portugal, Romania, Spain, USA. Most of the papers are in English, a few of them are in Spanish, Portuguese, or German.
Download or read book SCIENTIA MAGNA An international journal Vol 14 No 1 2019 written by Xiaolin Chen and published by Infinite Study. This book was released on with total page 106 pages. Available in PDF, EPUB and Kindle. Book excerpt: Scientia Magna is a peer-reviewed, open access journal that publishes original research articles in all areas of mathematics and mathematical sciences. However, papers related to Smarandache’s problems are highly preferred.
Download or read book CONSIDERATIONS ON NEW FUNCTIONS IN NUMBER THEORY written by Florentin Smarandache and published by Infinite Study. This book was released on with total page 20 pages. Available in PDF, EPUB and Kindle. Book excerpt: New functions are introduced in number theory, and for each one a general description, examples, connections, and references are given.
Download or read book Proceedings of the First International Conference on Smarandache Type Notions in Number Theory written by Constantine Dumitrescu and published by American Research Press. This book was released on 1997 with total page 211 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Generalized Partitions and New Ideas on Number Theory and Smarandache Sequences written by Amarnath Murthy and published by Infinite Study. This book was released on 2005-01-01 with total page 219 pages. Available in PDF, EPUB and Kindle. Book excerpt: Florentin Smarandache is an incredible source of ideas, only some of which are mathematical in nature. Amarnath Murthy has published a large number of papers in the broad area of Smarandache Notions, which are math problems whose origin can be traced to Smarandache. This book is an edited version of many of those papers, most of which appeared in Smarandache Notions Journal, and more information about SNJ is available at http://www.gallup.unm.edu/~smarandache/ . The topics covered are very broad, although there are two main themes under which most of the material can be classified. A Smarandache Partition Function is an operation where a set or number is split into pieces and together they make up the original object. For example, a Smarandache Repeatable Reciprocal partition of unity is a set of natural numbers where the sum of the reciprocals is one. The first chapter of the book deals with various types of partitions and their properties and partitions also appear in some of the later sections.The second main theme is a set of sequences defined using various properties. For example, the Smarandache n2n sequence is formed by concatenating a natural number and its double in that order. Once a sequence is defined, then some properties of the sequence are examined. A common exploration is to ask how many primes are in the sequence or a slight modification of the sequence. The final chapter is a collection of problems that did not seem to be a precise fit in either of the previous two categories. For example, for any number d, is it possible to find a perfect square that has digit sum d? While many results are proven, a large number of problems are left open, leaving a great deal of room for further exploration.
Download or read book The Smarandache Function written by Constantin Dumitrescu and published by Infinite Study. This book was released on 1996-01-01 with total page 137 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Applications of Smarandache Function Prime and Coprime Functions written by Sebastián Martín Ruiz and published by Infinite Study. This book was released on 2001 with total page 25 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Smarandache Notions Vol 10 written by V. Seleacu and published by Infinite Study. This book was released on 2000-08-01 with total page 211 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Palindromic Numbers and Iterations of the Pseudo Smarandache Function written by Charles Ashbacher and published by Infinite Study. This book was released on with total page 5 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper was originally published in Proceedings of the First International Coference on Smarandache Type Notions in Number Theory.
