| 广义Fermat数与伪素数 |
| |
| 引用本文： | 刘妙华,焦红英. 广义Fermat数与伪素数[J]. 重庆师范学院学报, 2014, 0(3): 55-57 |
| |
| 作者姓名： | 刘妙华 焦红英 |
| |
| 作者单位： | 空军工程大学理学院,西安710051 |
| |
| 摘 要： | 设m是正整数，b是正偶数，Gm=b^bm＋1。本文运用初等的方法证明了：i）Gm必为素数或者底为b的伪素数；ii）对于适合m1〈m2〈…〈mk的正整数m1，m2，…，mk，乘积Gm1Gm2…Gmk是底为b的伪素数的充要条件是mk≤b^m1-1。
|
| 关 键 词： | 广义Fermat数 乘积 伪素数 |
Generalized Fermat Numbers and Pseudoprimes |
| |
| LIU Miao-hua,JIAO Hong-ying. Generalized Fermat Numbers and Pseudoprimes[J]. Journal of Chongqing Normal University(Natural Science Edition), 2014, 0(3): 55-57 |
| |
| Authors: | LIU Miao-hua JIAO Hong-ying |
| |
| Affiliation: | (School of Science, Air Force Engineering University, Xi＇an 710051, China) |
| |
| Abstract: | Let Gm=bbm ＋1, where b and m are positive integers with 2 lb. In this paper, using certain elementary methods, we prove that： i） Gmis either a prime or a pseudoprime to base b;ii） Let m1 , m2 , …, mk be positive integers with m1〈m2 〈… mk. The product Gm1 Gm2 ...Gmk is a pseudoprime to base b if and only if mk≤bm1-1. |
| |
| Keywords: | generalized Fermat number product pseudoprime |
| 本文献已被 维普 等数据库收录！ |
|
