Proceedings Of The Fifth International Conference On Number Theory And Smarandache Notions Shangluo University China 2009

This Book is devoted to the proceedings of the Sixth International Conferenceon Number Theory and Smarandache Notions held in Tianshui during April 24-25,2010. The organizers were Prof. Zhang Wenpeng and Prof. Wangsheng He from Tianshui Normal University. The conference was supported by Tianshui Normal University and there were more than 100 participants.

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

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.

Third International Conference on Number Theory and Smarandache Problems, 23-25 March 2007, Weinan Teacher's University, China. Papers on Smarandache multi-spaces and mathematical combinatorics, Smarandache stepped functions, cube-free integers as sums of two squares, recurrences for generalized Euler numbers, the generalization of the primitive number function, the Smarandache LCM function and its mean value, a conjecture involving the F. Smarandache LCM function, a new arithmetical function and its asymptotic formula, and other similar topics. Contributors: J. Wang, A. Muktibodh, M. Selariu, X. Zhang, Y. Zhang, M. Liu, R. Zhang, S. Ma, L. Mao, and many others.