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关于 Smarandache 理论 及其有关问题 (On the Smarandache Notions and Related Problems), Volume 4

By Yu, Wang

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Book Id: WPLBN0002828164
Format Type: PDF (eBook)
File Size: 1.10 mb
Reproduction Date: 7/12/2013

Title: 关于 Smarandache 理论 及其有关问题 (On the Smarandache Notions and Related Problems), Volume 4  
Author: Yu, Wang
Volume: 4
Language: Chinese
Subject: Non Fiction, Education, Number Theory
Collections: Mathematics, Mathematical Analysis, Chinese Literature Collection, Arithmetic, Asian Literature Collection, Authors Community, Math, Technology, Education, Most Popular Books in China, Literature
Historic
Publication Date:
2013
Publisher: World Public Library
Member Page: Florentin Smarandache

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APA MLA Chicago

Yu, W., & Juanli, S. (2013). 关于 Smarandache 理论 及其有关问题 (On the Smarandache Notions and Related Problems), Volume 4. Retrieved from http://www.gutenberg.us/


Description
前言 数论这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. 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 in our country, the development of number theory is one of the oldest branches of mathematics and many well-known mathematical forward work on number theory in both the content of discourse, such as the common denominator, Pythagorean, some do not Equation given integer solution problems, and so….

Summary
This book will mainly be compiled by the research results of current domestic scholars on Smarandache notions and new problems, plus new problems posed by various scholars. Its main purpose is to introduce latest results about Smarandache notions and problems, including asymptotic properties of Smarandache function and related functions, identities and the solutions of special equations, and put forward to some new interesting problems. We hope that the readers could be interested in these issues. At the same time, this book could open up the reader’s perspective, guide and inspire the readers to these fields.

Table of Contents
第一章Smarandache函数的问题及其新进展1 1.1 引言. . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Smarandache非构造序列. . . . . . . . . . . . . . 1 1.3 Smarandache数字和. . . . . . . . . . . . . . . . 2 1.4 Smarandache数字乘积. . . . . . . . . . . . . . . 2 1.5 Smarandache Pierced链. . . . . . . . . . . . . . . 3 1.6 Smarandache因子乘积. . . . . . . . . . . . . . . 4 1.7 Smarandache真因子乘积. . . . . . . . . . . . . . 5 1.8 Smarandache平方补数. . . . . . . . . . . . . . . 6 1.9 Smarandache立方补数. . . . . . . . . . . . . . . 7 1.10 Smarandache广义剩余序列. . . . . . . . . . . . . 7 1.11 Smarandache素数列. . . . . . . . . . . . . . . . 8 1.12 Smarandache平方列. . . . . . . . . . . . . . . . 13 1.13 Smarandache素数可加补数. . . . . . . . . . . . . 15 1.14 Smarandache函数S(n) . . . . . . . . . . . . . . . 19 1.15 Smarandache双阶乘函数. . . . . . . . . . . . . . 31 1.16 Smarandache商函数. . . . . . . . . . . . . . . . 42 1.17 Smarandache p次幂原函数. . . . . . . . . . . . . . 43 1.18 第一类伪Smarandache素数. . . . . . . . . . . . . 43 1.19 第一类伪Smarandache平方数. . . . . . . . . . . . 44 1.20 Goldbach-Smarandache序列. . . . . . . . . . . . . 46 1.21 Vinogradov-Smarandache序列. . . . . . . . . . . . 46 1.22 Smarandache-Vinogradov序列. . . . . . . . . . . . 47 1.23 Smarandache-Logics序列. . . . . . . . . . . . . . 47 1.24 Smarandache-Position序列. . . . . . . . . . . . . . 48 1.25 Smarandache孪生素数. . . . . . . . . . . . . . . 48 1.26 Smarandache素数等式猜想. . . . . . . . . . . . . 51 1.27 Smarandache级数. . . . . . . . . . . . . . . . . 52 1.28 Smarandache Counter. . . . . . . . . . . . . . . . 53 1.29 Smarandache函数C(n) . . . . . . . . . . . . . . . 53 1.30 Smarandache函数G(n) . . . . . . . . . . . . . . . 54 目录 1.31 未解决的Smarandache问题1 . . . . . . . . . . . . . 57 1.32 未解决的Smarandache问题2 . . . . . . . . . . . . . 57 1.33 未解决的Smarandache问题3 . . . . . . . . . . . . . 58 1.34 未解决的Smarandache问题4 . . . . . . . . . . . . . 58 1.35 未解决的Smarandache问题5 . . . . . . . . . . . . . 58 1.36 未解决的Smarandache问题6 . . . . . . . . . . . . . 59 1.37 未解决的Smarandache问题7 . . . . . . . . . . . . . 61 1.38 未解决的Smarandache问题8 . . . . . . . . . . . . . 62 1.39 未解决的Smarandache问题9 . . . . . . . . . . . . . 62 1.40 未解决的Smarandache问题10 . . . . . . . . . . . . 62 1.41 未解决的Smarandache问题11 . . . . . . . . . . . . 63 1.42 未解决的Smarandache问题12 . . . . . . . . . . . . 64 1.43 未解决的Smarandache问题13 . . . . . . . . . . . . 65 1.44 未解决的Smarandache问题14 . . . . . . . . . . . . 70 第二章伪Smarandache函数. . . . . . . . . . . . . 72 2.1 引言. . . . . . . . . . . . . . . . . . . . . . . 72 2.2 伪Smarandache函数的基本定理. . . . . . . . . . . 73 2.3 关于伪Smarandache函数的问题. . . . . . . . . . . 75 第三章Kenichiro Kashihara博士的研究工作. . . . . . . . . . . . . 96 3.1 欧拉常数. . . . . . . . . . . . . . . . . . . . . 96 3.2 Smarandache群. . . . . . . . . . . . . . . . . . 96 3.3 连分数. . . . . . . . . . . . . . . . . . . . . . 97 3.4 伪Dirichlet素数分布. . . . . . . . . . . . . . . . 97 3.5 具有Smarandache系数的Dirichlet级数. . . . . . . . . 98 3.6 有序序列. . . . . . . . . . . . . . . . . . . . . 98 3.7 关于由Smarandache定义的序列的不等式. . . . . . . 101 3.8 关于由Smarandache定义的序列的极限. . . . . . . . 102 3.9 伪有序序列. . . . . . . . . . . . . . . . . . . . 102 3.10 关于素数平方分解为平方和问题. . . . . . . . . . . 103 3.11 素数组合. . . . . . . . . . . . . . . . . . . . . 104 3.12 p-进无理数. . . . . . . . . . . . . . . . . . . . 105 3.13 Diophantine方程. . . . . . . . . . . . . . . . . . 105 3.14 悖论. . . . . . . . . . . . . . . . . . . . . . . 110 关于Smarandache理论及其有关问题 第四章关于Smarandache函数的一些新注释. . . . . . . . . . . . . 111 4.1 引言. . . . . . . . . . . . . . . . . . . . . . . 111 4.2 Goldbach猜想的拓展. . . . . . . . . . . . . . . . 111 4.3 毗连型序列. . . . . . . . . . . . . . . . . . . . 113 4.4 拆分序列. . . . . . . . . . . . . . . . . . . . . 114 4.5 素数数位子序列. . . . . . . . . . . . . . . . . . 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. . . . . . . . . . . . . . . . . . 118 4.12 幂序列. . . . . . . . . . . . . . . . . . . . . . 118 4.13 伪阶乘序列. . . . . . . . . . . . . . . . . . . . 119 4.14 伪因子序列. . . . . . . . . . . . . . . . . . . . 120 4.15 伪偶数序列. . . . . . . . . . . . . . . . . . . . 120 4.16 伪奇数序列. . . . . . . . . . . . . . . . . . . . 121 4.17 伪倍数序列. . . . . . . . . . . . . . . . . . . . 122 4.18 伪triangular number序列. . . . . . . . . . . . . . 122 4.19 Smarandache-Kurepa 函数. . . . . . . . . . . . . . 122 4.20 Smarandache-Wagsta® 函数. . . . . . . . . . . . . 123 4.21 n阶Smarandache上取整函数. . . . . . . . . . . . . 123 4.22 Smarandache Near-To-Primordial 函数. . . . . . . . 124 参考文献. . . . . . . . . . . . . 125

 

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