Computer-aided Number Theory Problems On F.smarandache

It is well known the number theory is a discipline which studies the nature of integer, many important ideal and methods mostly in modern mathematics developed in study of the question number theory of unceasingly. Computer science is an applied science, developed from the last mid-century, firstly which is mainly used in scientific computing. With the development of the computer hardware and software technology, computer applied to solve math problems are more dispersive. Therefore, a lot of computer software is generated, and used to solve some mathematical problems. Of course, if by the help of computer's powerful calculation and derivation of the powerful capabilities, we study some number theory problems combined with elementary or analytic method, tend to get some unexpected results.In 1993, Florentin Smarandache the famous Romanian-American mathematician published a book entitled "Only Problems, Not Solutions" book. In this he presented 105 unsolved arithmetical problems and conjectures about these functions and sequences. which has caused a number of scholars'interest research, some issues and conjectures have been resolved, but others have not find a good solution.Based on the interest of Smarandache issue, this paper study of these issues and get some results, using some computer software, combined with elementary number theory, analytic number theory and other knowledge. The main achievements contained in this dissertation are as follows:1.Some problems in number theory, with the help of computer, we often obtain the unexpected results. The third chapter, we discusses how to use computer software to solve problems in number theory and related types of computer software and operation.2.The fourth chapter, shows how to use Mathematica, Maltab and C tools, combined with elementary and analytical method to obtain the solutions of the new equation3.The fifth chapter shows how to use Maltab mathematical Software and elementary method to study the problem on a number of non-k-power factor and the nature of its determinant...