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...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 proble...

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...RESEARCH ON SMARANDACHE PROBLEMS IN NUMBER THEORY (Collected papers) Edited by ZHANG WEN... ...RESEARCH ON SMARANDACHE PROBLEMS IN NUMBER THEORY (Collected papers) Edited by ZHANG WENPENG D... ... Hexis 200 4 RESEARCH ON SMARANDACHE PROBLEMS IN NUMBER THEORY (Collect ed papers) Edited by ... ... Hexis 200 4 RESEARCH ON SMARANDACHE PROBLEMS IN NUMBER THEORY (Collect ed papers) Edited by ZHANG W... ...ats.htm ISBN : 1 - 931233 - 88 - 8 Standard Address Number : 297 - 5092 Printed in the United States of America This book ... ...ory of Florentin Smarandache, who listed many new and unsolved problems in number theory. Contents Dedication v Preface xi An arithmetic function and... ...Florentin Smarandache, who listed many new and unsolved problems in number theory. Contents Dedication v Preface xi An arithmetic function and the pr... ... Contents Dedication v Preface xi An arithmetic function and the primitive number of power 1 Zhang Wenpeng On the primitive numbers of power and -po... ...its mean value 49 Gao Nan viii RESEARCH ON SMARANDACHE PROBLEMS IN NUMBER THEORY On the generalized constructive set 53 Gou su On the inferior and su...

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...This book contains 23 papers, most of which were written by participants to the fifth International Conference on Number Theory and Smarandache Notions held in Shangluo University, China, in March, 2009. In this Conference, several professors gave a talk on Smarandache Notions and many participants lectured on them both extensively and i...

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...3. Remarks Sandor [2] has considered the problem of finding the S-perfect and completely S-perfect numbers, but his proof is not complete. He has proved that the only S-perfect of the form n = p q is n = 6 and there is no S-perfect number of the form n = 2kq where k ¸ 2 is an integer and q is an odd prime. On the other han...

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...Cheng : An equation involving the Smarandache double factorial function and Euler function 8 A. A. K. Majumdar : S-perfect and completely S-perfect numbers 12 B. Zhao and S. Wang: Cyclic dualizing elements in Girard quantales 21 P. Chun and Y. Zhao : On an equation involving the Smarandache function and the Dirichlet divisor function 27 F. Li and Y. Wang : An equatio...

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...ook systematically introduces the works obtained by using analytic methods on Smarandache problems, the book includes the basic knowledge of analytic number theory, mean value on some Smarandache sequences, infinite series involving some Smarandache functions, hybrid mean value of divisor function and so on. This book could open up the reader’s perspective, and inspire th...

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A book on number theory.

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...门学科最初是从研究整数开始的, 所以叫做整数论. 后来整数 论又进一步发展, 就叫做数论了. 确切的说, 数论就是一门研究整数性质 的学科. 它是最古老的数学分支. 按照研究方法来说, 数论可以分成初等 数论, 解析数论, 代数数论, 超越数论, 计算数论, 组合数论等. Foreword Number theory, this discipline was originally started from the study integer, so called Number Theory. Later integer on further development of number theory called it. Rather, number theory is an integer nature of disciplines...

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...的皇后, 数论是数学中的皇冠”. 虽然数论中的许多问题在很早就开始了研究, 并得到了丰硕的成果, 但是至今仍有许多被数学家称之为“皇冠上的明 珠”的悬而未解的问题等待人们去解决. 正因如此, 数论才能不断地充 实和发展, 才能既古老又年轻, 才能始终活跃在数学领域的前沿. Foreword Number theory, this discipline was originally started from the study integer, so called integer number theory. Later integer further development of number theory, number theory called up. Rather, number theory is an integer o...

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...eme Smarandache etc. Cartea poate fi descărcată din site-ul. During the period 24 to 25 April 2010 was conducted Sixth International Conference on Number Theory and Smarandache Notions of Tianshui Normal University, China. Conference organizers were prof. Dr. Zhang Wenpeng together from Northwest University in Xi'an and prof. Dr. Wangsheng He Tianshui Normal University....

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...的, 所以叫做整数论. 后来整数 论又进一步发展, 就叫做数论了. 确切的说, 数论就是一门研究整数性质 的学科. 在我国, 数论也是发展最早的数学分支之一. 许多著名的数学著 作中都有关于数论内容的论述, 比如求最大公约数、勾股数组、某些不 定方程整数解的问题等等... Foreword Number theory, this discipline was originally started from the study integer, so called Number Theory. Later integer on further development of number theory called it. Rather, number theory is an integer nature of Discipline ...

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...序列. . . . . . . . . . . . . . . . . . 114 4.6 完全幂的特殊表达式. . . . . . . . . . . . . . . . 114 4.7 广义周期序列. . . . . . . . . . . . . . . . . . . 115 4.8 Numberical Carpet序列. . . . . . . . . . . . . . . 115 4.9 筛序列. . . . . . . . . . . . . . . . . . . . . . 116 4.10 Syllabic Puzzle序列. . . . . . . . . . . . . . . . . 118 4.11 Code Puzzle序列. . . . . . . . . . . . . . . . . . ...

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...Library (Romania), and Archives of State (Rm. Valcea, Romania). The Smarandache's universe is undoubtedly very fascinating and is halfway between the number theory and the recreational mathematics. Even though sometime this universe has a very simple structure from number theory standpoint, it doesn't cease to be deeply mysterious and interesting. This book, following the ...

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...A SET OF NEW SMARANDACHE FUNCTIONS, SEQUENCES AND CONJECTURES IN NUMBER THEORY Felice Russo AMERICAN RESEARCH PRESS Lupton USA 2000 Wrongnes... ...A SET OF NEW SMARANDACHE FUNCTIONS, SEQUENCES AND CONJECTURES IN NUMBER THEORY Felice Russo AMERICAN RESEARCH PRESS Lupton USA 2000 Wrongness of n ... ...ache's universe is undoubtedly very fascinating and is halfway between the number theory and the recreational mathematics. Even though sometime this ... ...universe is undoubtedly very fascinating and is halfway between the number theory and the recreational mathematics. Even though sometime this univers... ...tics. Even though sometime this universe has a very simple structure from number theory standpoint, it doesn't cease to be deeply mysterious and inte... ...Even though sometime this universe has a very simple structure from number theory standpoint, it doesn't cease to be deeply mysterious and interesting... ...ed problems, new Smarandache type sequences and new Smarandache Notions in number theory. Moreover a chapter (IV) is dedicated to the analysis of Sma... ...lems, new Smarandache type sequences and new Smarandache Notions in number theory. Moreover a chapter (IV) is dedicated to the analysis of Smarandach... ...ted to the analysis of Smarandache Double factorial function introduced in number theory by F. Smarandache ("The Florentin Smarandache papers" specia...

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...athematical Spectrum, VoL 29, No 1. It concerns what happens when an operation applied to an n-digit integer results in an n digit integer. Since the number of ndigit integers is finite a repetition must occur after applying the operation a finite number of times. It was assumed in the above article that this would lead to a periodic sequence which is not always true becau...

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... the book a good one becomes the responsibility of the author. The Smarandache function is simultaneously a logical extension to earlier functions in number theory as well as a key to many future paths of exploration. As such, it is hoped that you get as much out of this book as the author did in writing it. While all books are a collective work, the responsibility for a...

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...As one of the oldest of mathematical disciplines, the roots of number theory extend back into antiquity. Problems are often easy to state, but extremely difficult to solve. Which is the origin of much of their charm. All mathematicians, amateurs and professionals alike, have a soft sp...

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...This issue of the journal is devoted to the proceedings of the third International Conference on Number Theory and Smarandache Problems. The conference was a great success and will give a strong impact on the development of number theory in general and Smarandache problems in particular. In this volume we assemble not on...

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...thods to study the asymptotic properties of Sk(n), and give an interesting asymptotic formula for it. Keywords : F. Smarandache problem, primitive numbers, asymptotic formula. ...

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...J. Wang : Cube-free integers as sums of two squares 1 G. Liu and H. Li : Recurrences for generalized Euler numbers 9 H. Li and Q. Yang : Some properties of the LCM sequence 14 M. Liu : On the generalization of the primitive number function 18 Z. Lv : On the F. Smarandache LCM function and its mean value 22 Q. Wu : A conjecture...

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...This is a book on empirical number theory concentrating on the analysis of number sequences. Its focus is on a small part of a very large number of integer sequences defined by Florentin Smarandache. The author has. however. when appropriate included so...

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..., Padilla treated the Smarandache algebraic structures mainly with associative binary operation. Since then the subject has been pursued by a growing number of researchers and now it would be better if one gets a coherent account of the basic and main results in these algebraic structures. This book aims to give a systematic development of the basic non-associative algebra...

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...eBooks-otherformats.htm ISBN: 1-931233-61-6 Standard Address Number: 297-5092 Printed in the United States of America 3 ... ...ciative binary operation. Since then the subject has been pursued by a growing number of researchers and now it would be better if one gets a coheren... ...d of algebraic structures like semigroup, group etc. and a good foundation in number theory. In Chapter 1 we just recall the basic notations and s... ...lgebraic structures like semigroup, group etc. and a good foundation in number theory. In Chapter 1 we just recall the basic notations and some imp... ...ed to lessen the non abstractness of this structure. In this chapter, several number theoretic techniques are used. Chapter 4 starts with the def... ...e = e ∗ a = a for all a ∈ G. We call the order of the groupoid G to be the number of distinct elements in it denoted by o(G) or |G|. If the numbe... ...nger Verlag, (1958). 2. Ivan Nivan and H.S.Zukerman, Introduction to number theory, Wiley Eastern Limited, (1989). 3. W.B. Vasantha Kandasamy, ... ...d Kama. Her current interests include Smarandache algebraic structures, fuzzy theory, coding/ communication theory. In the past decade she has guide... ...cholars in the different fields of non-associative algebras, algebraic coding theory, transportation theory, fuzzy groups, and applications of fuzzy...

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... and to learn to handle it in an (un)usual way. To transform the apparently unscientific ideas into scientific ones, and to develop their study (The Theory of Imperfections). And finally, to interconnect opposite (and not only) human fields of knowledge into a.s-heterogeneous-as-possible another fields. The author welcomes any co=ents, notes, articles on this paper and/...

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...sum", said Rene Descartes, "I doubt, therefore I think; I think, therefore I exist" (metaphysical doubt). See what happens if you deny the classics' theory?...

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...atics [Anti-Mathematics, Multi-Structure and Multi-Space, Space of Non-Integer or Negative Dimention, Inconsistent Sysytem ofAxiomas or Contradictory Theory, Non-Euclidean Geometries: Paradoxist Geometry, Non-Geometry, CounterProjective Geometry and Counter-Axioms, Anti-Geometry and Anti-Axioms, Model of an Anti-Geometry, Discontinuous Geometries] 5 -- Logica sau iogica Ma...