| 摘要: |
| 对任一奇素数p和正整数n，给出满足xp－1≡1(modpn)的解的一般表达式，推广了华罗庚关于费马解的概念，得到了任意奇素数p都存在无穷多个任意n次费马解及其相关性质. |
| 关键词: 费马解 n次费马解 通解 证明 |
| DOI： |
| 分类号:O156.1 |
| 基金项目:贵州省教育厅优秀科技创新人才项目（黔教合KY字\[2013\]153）；湖南省自然科学基金资助项目（14JJ7047）；凯里学院博士教授启动基金项目（BS201309） |
|
| Explore and prove about the general solution of Fermat Solution |
|
Yang Xiaobin1，Yuan Zihan21,2
|
|
1.College of Mathematical Science, Kaili University, Kaili 556011,China;2.College of Mathematics and Computational Science, Hunan University of Science and Technology, Xiangtan 411201, China
|
| Abstract: |
| For p is an odd prime numbers, n is a positive integer. The formula of general solution was given that meet the condition xp－1≡1(modpn), and the concept of Hua Luogeng about Fermat’s solution was promoted. In addition, a conclusion was come to that: there are an infinite Fermat’s solutions for any power of n, and the involved nature of Fermat’s solution was proved. |
| Key words: Fermat’s solution Fermat’s solutions for any power of n general solution prove |
