3阶Carmichael数(英文)  

Carmichael Numbers of Order 3

作　　者：朱文余[1] 孙琦[1] 

机构地区：[1]四川大学数学学院,成都610064

出　　处：《四川大学学报（自然科学版）》2005年第1期47-51,共5页Journal of Sichuan University(Natural Science Edition)

基　　金：国家自然科学基金(10128103)

摘　　要：设Ck(k>0)表示k阶Carmichael数集,C1即为通常的Carmichael数集.作者考虑3阶Carmichael数的性质,得到了n∈C3的一个必要条件(定理1)和两个容易计算的充分条件(定理2和定理3).对于108以下,发现了43个3阶Carmichael数.同时,验证了在108以下不存在满足定理2中条件的3阶Carmichael数,以及在104以下仅有3个3阶Carmichael数:1885,2101,9529.还证明了C1 C3以及C2 C3,部分回答了RajatBhattacharjee等提出的一个问题.对于3阶Carmichael数,作者提出了三个未解决的问题.Let C_k(k>0) denote the set of Carmichael numbers of order k and C_1 be the set of the standard Carmichael numbers. In this paper, the authors consider C_3 and get a necessary condition for Carmichael numbers of order 3. Two easily computable sufficient conditions for Carmichael numbers of order 3 are also given. The authors find 43 Carmichael numbers of order 3 less than 10~8 and it is verified that one type of Carmichael numbers of order 3 less than 10~8 does not exist (Theorem 2), and they prove that there are only three Carmichael numbers of order 3 less than 10~4, which are 1885, 2101, 9529. Furthermore, they prove that C_1C_3 and C_2C_3, which gives a partial answer to an unknown problems.

关 键 词：CARMICHAEL数 广义Carmichael数 Zn[x]上的不可约多项式 

分 类 号：O156.2[理学—数学]