On Some of the Smarandache's Problems

School Science and Mathematics, Mar 2003 by Rahim, Medhat H

Author

Krassimir T. Atanassov American Research Press 140 & Window Rock Road Box 199 Lupton, AZ 86508

1999; 88 pages Paperback

This text is in microfilm format, and can be ordered from:

University of Microfilm International 300 N. Zeeb Road, P.O. Box 1346 Ann Arbor MI 48106-1346, USA, Tel.: 1-800-521-0600

Reviewer

Medhat H. Rahim Lakehead University Thunder Bay, Ontario, Canada, P7B 5E1

The 88-page text, On Some of the Smarandache's Problems, contains 16 sections, each ofwhich consists of an article in the form of solutions of one, two, three, or four of Florentin Smarandache's unsolved proposed problems.

The text covers 27 Smarandache's problems solved by the author and selected from two sources of unsolved Smarandache's problems: (a) Smarandache, F., (1993), Only Problems, Not Solutions! Xiquan Publications House, Chicago, USA; and (2) Dumitrescu, C., & Seleacu,,V., (1994), Some Solutions and Questions in Number Theory. Erhus University Press, Glendale.

The author states that in 1996 and while he was writing book reviews for the books (a) containing 105 unsolved problems and (b) containing 140 unsolved problems, he found himself in contact for the first time with Smarandache's unsolved problems. Since then he became interested in this area of research. In 1998, the author started his work attempting to solve some of Smarandache's problems. He ended with this exciting volume of solutions for 27 problems proposed by Smarandache. The author's love of Number Theory and his high level of dedication to his profession took him into the product of this interesting, exciting, and nontrivial work. The hard work and distinct ability of this brilliant mathematician guided him to introduce proofs for some of the problems, modifications and counterexamples for others.

It is interesting to reflect on the joy and worries of this great mathematician while working on Smarandache's unsolved problems. The author states that when this text was finished and was ready for publication, he received from "Zentralblatt fur Mathematik" another text for review written by Charles Ashbacher (Ashbacher, C., 1998, Pluckings from the Tree of Smarandache Sequence and Functions. American Research press, Lupton, AZ). It was of his great delight to find out, while reviewing the new book, that only five of the problems he had worked out were discussed in the text he received and that their approaches were different.

The author ofthis text is hoping to prove some other unsolved problems in the future. As the reality of the mathematicians' profession suggests, there exist problems for which it is not certain whether solutions will be found within the next fewyears or will share the destiny of Fermat's Last Theorem!

Editor's Note: S. Wali Abdi's postal address is The University of Memphis, Department of Instruction and Curriculum Leadership, 401 A Ball Hall, Memphis, TN 38152,and e-mail address is abdi.wali@coe.memphis.edu.