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Zhang Wenpeng, "Research on Smarandache Problems in Number Theory,Vol.1-2 "

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 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 Dr. Zhang Wenpeng's students. After this chance, they will be more interested in the mysterious integer and number theory!

More future papers by his students will focus on the Smarandache notions, such as sequences, functions, constants, numbers, continued fractions, infinite products, series, etc. in number theory!

Volume 2:

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.

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