Download or read book On the solutions of an equation involving the Smarandache function written by Lu Yaming and published by Infinite Study. This book was released on with total page 4 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper, we discussed the solutions of the following equation involving the Smarandache function.
Download or read book On the solvability of an equation involving the Smarandache function and Euler function written by Weiguo Duan and published by Infinite Study. This book was released on with total page 10 pages. Available in PDF, EPUB and Kindle. Book excerpt: For any positive integer n, the famous F.Smarandache function S(n) is defined as the smallest positive integer m such that n divides m!.
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 ON SOME VALUES OF THE SANDOR SMARANDACHE FUNCTION written by A.A.K. Majumdar and published by Infinite Study. This book was released on with total page 11 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper finds SS(n) for some particular cases of n.
Download or read book A generalization of the Smarandache function written by Hailong Li and published by Infinite Study. This book was released on with total page 4 pages. Available in PDF, EPUB and Kindle. Book excerpt: This function is a generalization of the famous Smarandache function S(n). The main purpose of this paper is using the elementary and analytic methods to study the mean value properties of P(n), and give two interesting mean value formulas for it.
Download or read book An Introduction to the Smarandache Function written by Charles Ashbacher and published by Infinite Study. This book was released on 1995 with total page 62 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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 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 Plucking from the Tree of Smarandache Functions and Sequences written by Charles Ashbacher and published by Infinite Study. This book was released on 1998-01-01 with total page 80 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Smarandache Function Journal vol 7 1996 written by V. Seleacu and published by Infinite Study. This book was released on with total page 154 pages. Available in PDF, EPUB and Kindle. Book excerpt: A collection of papers concerning Smarandache type functions, numbers, sequences, inteqer algorithms, paradoxes, experimental geometries, algebraic structures, neutrosophic probability, set, and logic, etc.
Download or read book An Algorithm for Calculating Smarandache s Function and Wich Using Legendre s Formula written by Tatiana-Corina Dosescu and published by Infinite Study. This book was released on with total page 10 pages. Available in PDF, EPUB and Kindle. Book excerpt: The paper presents a calculation algorithm for the values of the function S, defined by Fl. Smarandache [6], [1], [4], [5], an algorithm that uses the writing of numbers in base ten and it is based on Legendre's formula and some theoretical results. It differs from the one presented in [8], which avoids factorization, and from the one presented in [6], which requires writing on a generalized basis. Then a characterization of a prime number is given. Finally, a numerical application is presented.The paper presents a calculation algorithm for the values of the function S, defined by Fl. Smarandache [6], [1], [4], [5], an algorithm that uses the writing of numbers in base ten and it is based on Legendre's formula and some theoretical results. It differs from the one presented in [8], which avoids factorization, and from the one presented in [6], which requires writing on a generalized basis. Then a characterization of a prime number is given. Finally, a numerical application is presented.
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 Function Journal vol 9 1998 written by V. Seleacu and published by Infinite Study. This book was released on with total page 158 pages. Available in PDF, EPUB and Kindle. Book excerpt: A collection of papers concerning Smarandache type functions, numbers, sequences, inteqer algorithms, paradoxes, experimental geometries, algebraic structures, neutrosophic probability, set, and logic, etc.
Download or read book Smarandache Notions Vol 7 written by C. Dumitrescu and published by Infinite Study. This book was released on 2000-08-01 with total page 155 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Scientia Magna Vol 3 No 2 2007 written by Zhang Wenpeng and published by Infinite Study. This book was released on with total page 119 pages. Available in PDF, EPUB and Kindle. Book excerpt: Papers on subclass of analytic and univalent functions in the unit disk, large quaternary cyclic codes of length 85 and related quantum error-correcting, value distribution of the Smarandache LCM function, chains of inequalities, some identities involving the near pseudo Smarandache function, and other similar topics. Contributors: S. M. Khairnar, M. More, Y. Ma, J. Chen, M. Bencze, C. Tian, N. Yuan, J. Caltenco, M. Enciso-Aguilar, W. Zheng, J. Dou, and many others.
Download or read book Scientia Magna Vol 4 No 2 2008 written by Zhang Wenpeng and published by Infinite Study. This book was released on with total page 132 pages. Available in PDF, EPUB and Kindle. Book excerpt: Papers on two problems related to the Smarandache function, the additive k-power complements, the generalization of sequence of numbers with alternate common differences, an equation related to the Smarandache function and its positive integer solutions, the pseudo Smarandache square-free function, and other similar topics. Contributors: W. Zhang, Y. Guo, W. Xiong, S. Yilmaz, M. Turgut, A. A. Majumdar, B. Ahmad, J. Zhang, P. Zhang, N. Dung, and many others.
Download or read book Scientia Magna Vol 2 No 3 2006 written by Zhang Wenpeng and published by Infinite Study. This book was released on with total page 119 pages. Available in PDF, EPUB and Kindle. Book excerpt: Papers on the Pseudo-Smarandache function, primes in the Smarandache deconstructive sequence, recursion formulae for Riemann zeta function and Dirichlet series, parastrophic invariance of Smarandache quasigroups, certain inequalities involving the Smarandache function, and other similar topics. Contributors: A. Majumdar, S. Gupta, S. Zhang, C. Chen, A. Muktibodh, J. Sandor, M. Karama, A. Vyawahare, H. Zhou, and many others.
