Research on Smarandache Problems in Number Theory (collected papers), Vol. I

Research on Smarandache Problems in Number Theory (collected papers), Vol. I PDF Author: Wenpeng Zhang
Publisher: Infinite Study
ISBN: 1931233888
Category : Mathematics
Languages : en
Pages : 178

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Book Description
Number theory is an ancient subject, but we still cannot answer many simplest and most natural questions about the integers. Some old problems have been solved, but more arise. All the research for these ancient or new problems implicated and are still promoting the development of number theory and mathematics.American-Romanian number theorist Florentin Smarandache introduced hundreds of interest sequences and arithmetical functions, and presented many problems and conjectures in his life. In 1991, he published a book named Only problems, Not solutions!. He presented 105 unsolved arithmetical problems and conjectures about these functions and sequences in it. Already many researchers studied these sequences and functions from his book, and obtained important results.This book, Research on Smarandache Problems in Number Theory (Collected papers), contains 41 research papers involving the Smarandache sequences, functions, or problems and conjectures on them.All these papers are original. Some of them treat the mean value or hybrid mean value of Smarandache type functions, like the famous Smarandache function, Smarandache ceil function, or Smarandache primitive function. Others treat the mean value of some famous number theoretic functions acting on the Smarandache sequences, like k-th root sequence, k-th complement sequence, or factorial part sequence, etc. There are papers that study the convergent property of some infinite series involving the Smarandache type sequences. Some of these sequences have been first investigated too. In addition, new sequences as additive complement sequences are first studied in several papers of this book.Most authors of these papers are my students. After this chance, I hope they will be more interested in the mysterious integer and number theory!More future papers by my students will focus on the Smarandache notions, such as sequences, functions, constants, numbers, continued fractions, infinite products, series, etc. in number theory!List of the Contributors:Zhang Wenpeng, Xu Zhefeng, Zhang Xiaobeng, Zhu Minhui, Gao Nan, Guo Jinbao, He Yanfeng, Yang Mingshun, Li Chao, Gao Jing, Yi Yuan, Wang Xiaoying, Lv Chuan, Yao Weili, Gou Su, He Xiaolin, Li Hailong, Liu Duansen, Li Junzhuang, Liu Huaning, Zhang Tianping, Ding Liping, Li Jie, Lou Yuanbing, Zhao Xiqing, Zhao Xiaopeng, Yang Cundian, Liang Fangchi

Research on Smarandache Problems in Number Theory (collected papers), Vol. I

Research on Smarandache Problems in Number Theory (collected papers), Vol. I PDF Author: Wenpeng Zhang
Publisher: Infinite Study
ISBN: 1931233888
Category : Mathematics
Languages : en
Pages : 178

Get Book Here

Book Description
Number theory is an ancient subject, but we still cannot answer many simplest and most natural questions about the integers. Some old problems have been solved, but more arise. All the research for these ancient or new problems implicated and are still promoting the development of number theory and mathematics.American-Romanian number theorist Florentin Smarandache introduced hundreds of interest sequences and arithmetical functions, and presented many problems and conjectures in his life. In 1991, he published a book named Only problems, Not solutions!. He presented 105 unsolved arithmetical problems and conjectures about these functions and sequences in it. Already many researchers studied these sequences and functions from his book, and obtained important results.This book, Research on Smarandache Problems in Number Theory (Collected papers), contains 41 research papers involving the Smarandache sequences, functions, or problems and conjectures on them.All these papers are original. Some of them treat the mean value or hybrid mean value of Smarandache type functions, like the famous Smarandache function, Smarandache ceil function, or Smarandache primitive function. Others treat the mean value of some famous number theoretic functions acting on the Smarandache sequences, like k-th root sequence, k-th complement sequence, or factorial part sequence, etc. There are papers that study the convergent property of some infinite series involving the Smarandache type sequences. Some of these sequences have been first investigated too. In addition, new sequences as additive complement sequences are first studied in several papers of this book.Most authors of these papers are my students. After this chance, I hope they will be more interested in the mysterious integer and number theory!More future papers by my students will focus on the Smarandache notions, such as sequences, functions, constants, numbers, continued fractions, infinite products, series, etc. in number theory!List of the Contributors:Zhang Wenpeng, Xu Zhefeng, Zhang Xiaobeng, Zhu Minhui, Gao Nan, Guo Jinbao, He Yanfeng, Yang Mingshun, Li Chao, Gao Jing, Yi Yuan, Wang Xiaoying, Lv Chuan, Yao Weili, Gou Su, He Xiaolin, Li Hailong, Liu Duansen, Li Junzhuang, Liu Huaning, Zhang Tianping, Ding Liping, Li Jie, Lou Yuanbing, Zhao Xiqing, Zhao Xiaopeng, Yang Cundian, Liang Fangchi

Research on Smarandache Problems in Number Theory (collected papers), Vol. II

Research on Smarandache Problems in Number Theory (collected papers), Vol. II PDF Author: Wenpeng Zhang
Publisher: Infinite Study
ISBN: 1931233993
Category : Mathematics
Languages : en
Pages : 157

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Book Description
This book contains 34 papers, most of which were written by participants to the First Northwest Number Theory Conference held in Shangluo Teacher?s College, China, in March, 2005. In this Conference, several professors gave a talk on Smarandache Problems and many participants lectured on them both extensively and intensively. All these papers are original and have been refereed. The themes of these papers range from the mean value or hybrid mean value of Smarandache type functions, the mean value of some famous number theoretic functions acting on the Smarandache sequences, to the convergence property of some infinite series involving the Smarandache type sequences.

The Math Encyclopedia of Smarandache type Notions

The Math Encyclopedia of Smarandache type Notions PDF Author: Marius Coman
Publisher: Infinite Study
ISBN: 1599732521
Category :
Languages : en
Pages : 136

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Book Description
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.

Scientia Magna, vol. 2, no. 4, 2006

Scientia Magna, vol. 2, no. 4, 2006 PDF Author: Zhang Wenpeng
Publisher: Infinite Study
ISBN: 1599730219
Category :
Languages : en
Pages : 123

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Book Description
Papers on Smarandache inversion sequence, global attractivity of a recursive sequence, Smarandache fantastic ideals of Smarandache BCI-algebras, translational hull of superabundant semigroups with semilattice of idempotents, the Universality of some Smarandache loops of Bol-Moufang type, and other similar topics. Contributors: M. Karama, P. Zhang, W. Kandasamy, M. Khoshnevisan, K. Ilanthenral, M. Bencze, H. Ibstedt, W. Zhu, J. Earls, and many others.

SCIENTIA MAGNA: An international journal, Vol. 13, No. 1, 2018

SCIENTIA MAGNA: An international journal, Vol. 13, No. 1, 2018 PDF Author: Richa Brar
Publisher: Infinite Study
ISBN:
Category : Mathematics
Languages : en
Pages : 187

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Book Description
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 will be highly preferred.

SCIENTIA MAGNA – International Book Series (vol. 13, no. 1)

SCIENTIA MAGNA – International Book Series (vol. 13, no. 1) PDF Author: Huaning Liu
Publisher: Infinite Study
ISBN:
Category : Mathematics
Languages : en
Pages : 188

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Book Description
Scientia Magna international book series are published in one or two volumes per year with more than 100 pages and over 1,000 copies.

Scientia Magna, Vol. 2, No. 1, 2006

Scientia Magna, Vol. 2, No. 1, 2006 PDF Author: Zhang Wenpeng
Publisher: Infinite Study
ISBN: 159973009X
Category : Science
Languages : en
Pages : 120

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Book Description
Collection of papers from various scientists dealing with Smarandache Notions in science. Papers on holomorphic study of the Smarandache concept in loops, some arithmetical properties of primitive numbers of power p, Smarandache quasigroups, the mean value of the Smarandache simple divisor function, and other similar topics. Contributors: Z. Xu, Y. Shao, X. Zhao, X. Pan, T. Kim, C. Adiga, J. Han, Q. Yang, and many others.

On Some of the Smarandache Problems, Vol. II

On Some of the Smarandache Problems, Vol. II PDF Author: Mladen V. Vassilev-Missana
Publisher: Infinite Study
ISBN: 1931233896
Category : Mathematics
Languages : en
Pages : 67

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Book Description
Five years after having published the first volume, the authors obtained many new results related to Smarandaches Problems. They are collected in this book and deal with Smarandache sequences, infinite numbers, functions, formulas, conjunctures in Number Theory.

Collected Papers. Volume I

Collected Papers. Volume I PDF Author: Florentin Smarandache
Publisher: Infinite Study
ISBN: 1599730480
Category : Mathematics
Languages : en
Pages : 229

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Book Description
Articles, notes, generalizations, paradoxes, miscellaneous in mathematics, linguistics, and education.

Scientia Magna, Vol. 1, No. 2, 2005

Scientia Magna, Vol. 1, No. 2, 2005 PDF Author: Zhang Wenpeng
Publisher: Infinite Study
ISBN: 1599730022
Category : Science
Languages : en
Pages : 203

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Book Description
Collection of papers from various scientists dealing with smarandache notions in science.