Description Details
...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...

Full Text Search Details
...RESEARCH ON SMARANDACHE PROBLEMS IN NUMBER THEORY (Collected papers) Edited by ZHANG WEN... ... Hexis 200 4 RESEARCH ON SMARANDACHE PROBLEMS IN NUMBER THEORY (Collect ed papers) Edited by ... ...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... ... 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... ...randache irrational root sieve sequences 27 Zhang Xiaobeng, Lou Yuanbing A number theoretic function and its mean value 33 Lv Chuan On the primitive n... ...ao Weili On the inferior and superior factorial part sequences 47 Li Jie A number theoretic function and its mean value 49 Gao Nan viii RESEARCH ON S... ...on and 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... ...unctions 69 Liu Huaning, Gao Jing On the Smarandache ceil function and the number of prime factors 73 Xu Zhefeng On the mean value of an arithmetical ...

Description Details
...on, and am(n) denotes the Smarandache m-th power residues function of n. The main purpose of this paper is using the elementary method to study the number of the solutions of the equation (n) = am(n), and give all solutions for this equation....

Full Text Search Details
...NZHUANG, LIU DUANSEN (EDITORS) RESEARCH ON SMARANDACHE PROBLEMS IN NUMBER THEORY (VOL. II) PROCEEDINGS OF THE FIRST NORTHWEST CONFERENCE ... ...BER THEORY (VOL. II) PROCEEDINGS OF THE FIRST NORTHWEST CONFERENCE ON NUMBER THEORY Hexis Phoenix, AZ 2005 EDITORS: ZHA... ... SHANGLUO, SHAANXI, P.R.CHINA RESEARCH ON SMARANDACHE PROBLEMS IN NUMBER THEORY (VOL. II) PROCEEDINGS OF THE FIRST NORTHWEST CONFERENCE ... ...BER THEORY (VOL. II) PROCEEDINGS OF THE FIRST NORTHWEST CONFERENCE ON NUMBER THEORY Hexis Phoenix, AZ 2005... ...ormats.htm ISBN: 1-931233-99-3 Standard Address Number: 297-5092 Printed in the United States of America Contents Dedi... ...OntheSmarandache Riemannzetasequence 29 Li Jie Onthepropertiesofthehexagon numbers 33 LiuYanni Onthemeanvalueofthek thpowerpartresiduefunction 37 MaJi... ...fessor Florentin Smarandache, who listed many new and unsolved problems in number theory. Preface Arithmetic is where numbers run across your mind... ...e numbers run across your mind looking for the answer. Arithmetic is like numbers spinning in your head faster and faster until you blow up with the... ... Nathanson Mathematics is often referred to as a servant of science and number theory as a queen of mathematics, by which we are to understand tha...

Description Details
...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...

Excerpt Details
...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...

Table of Contents Details
...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...

Description Details
...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...

Description Details
A book on number theory.

Description Details
...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...

Excerpt Details
...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...

Description Details
...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 ...

Table of Contents Details
...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. . . . . . . . . . . . . . . . . . ...

Description Details
...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....

Description Details
...e Root Spiral ( or “Spiral of Theodorus” or “Einstein Spiral” ) is a very interesting geometrical structure in which the square roots of all natural numbers have a clear defined orientation to each other. This enables the attentive viewer to find many spatial interdependencies between natural numbers, by applying simple graphical analysis techniques. Therefore the Square...

Excerpt Details
...Another striking property of the Square Root Spiral is the fact, that the square roots of all square numbers ( 4, 9, 16, 25, 36… ) lie on 3 highly symmetrical spiral graphs which divide the square root spiral into 3 equal areas. ( see FIG.1 : graphs Q1, Q2 and Q3 drawn in green color )....

Description Details
...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...

Description Details
...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 ...

Full Text Search Details
...A SET OF NEW SMARANDACHE FUNCTIONS, SEQUENCES AND CONJECTURES IN NUMBER THEORY Felice Russo AMERICAN RESEARCH PRESS Lupton USA 2000 Wrongnes... ...ache's universe is undoubtedly very fascinating and is halfway between the number theory and the recreational mathematics. Even though sometime this ... ...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... ...ed problems, new Smarandache type sequences and new Smarandache Notions in number theory. Moreover a chapter (IV) is dedicated to the analysis of Sma... ...ted to the analysis of Smarandache Double factorial function introduced in number theory by F. Smarandache ("The Florentin Smarandache papers" specia... ...by F. Smarandache. In particular we will analyse some conjectures on prime numbers and the generalizations of Goldbach conjecture. This book would be ... ...s start our observation. 4 Chapter I On some new Smarandache functions in Number Theory. A number-theoretic function is any function which is defined... ..., as are n!, º ß n , 2 n etc. The functions which are interesting from number theory point of view are, of course, those like (n) j whose value de... ...argument increases. In the 1970's F. Smarandache created a new function in number theory whose behaviour is highly irregular like the (n) j function. ...

Description Details
...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...

Full Text Search Details
...Generalized Partitions and New Ideas On Number Theory and Smarandache Sequences Editor’s Note This ... ...PIDS, IOWA 42402 USA GENERALIZED PARTITIONS AND SOME NEW IDEAS ON NUMBER THEORY AND SMARANDACHE SEQUENCES H... ...la and Charles Ashbacher ISBN: 1-931233-34-9 Standard Address Number: 297-5092 Printed in the United States of America 3 Editor... ...s, Sequences and Functions ………………. 11 1.2 A Program to Determine the Number of Smarandache Distinct Reciprocal Partitions of Unity of a Give... ...dache Factor Partitions ………………… 62 1.14 A Program For Determining the Number of SFPs ………………… 64 1.15 Chapter References ………………… 70 Chapte... ... Chapter 2 Smarandache Sequences ………………… 72 2.1 On the Largest Balu Number and Some SFP Equations ………………… 72 2.2 Smarandache Pascal Derived... ...f the the Depascalization Theorem ………………… 83 2.5 Smarandache Friendly Numbers and A Few More Sequences ………………… 86 2.6 Some New Smarandache ... ... Sequence ………………… 101 2.11 Decomposition of the Divisors of A Natural Number Into Pairwise Co- Prime Sets ………………… 103 2.12 On the Divisors of ... ...…………… 106 2.13 Smarandache Dual Symmetric Functions and Corresponding Numbers of the Type of Stirling Numbers of the First Kind ………………… 108 ...

Description Details
...has seated the self in the state of pure Self (Shuddhatma) in just two hours through the unique method of the Gnan Vidhi and acquainted You with file number one, also called as ‘Chandubhai,Your closest file.Now, if You want to attain liberation in one more life, then maintain separation with ‘Chandubhai’. And for that He explains the science and art of conversing with file...

Description Details
...has seated the self in the state of pure Self (Shuddhatma) in just two hours through the unique method of the Gnan Vidhi and acquainted You with file number one, also called as ‘Chandubhai,Your closest file. It is this file that prevents Your moksha (final liberation). Now, if You want to attain liberation in one more life, then maintain separation with ‘Chandubhai’. And f...