关于3阶Carmichael数(英文)  

On Carmichael Numbers of Order 3

作　　者：刘亚[1] 金正平[1] 

机构地区：[1]安徽师范大学数学系,芜湖安徽241000

出　　处：《数学进展》2008年第4期478-482,共5页Advances in Mathematics（China）

基　　金：NSFC(No.10071001);SF of Anhui Province Grant(No.01046103);the SF of the Education Department of Anhui Province Grant(No.2002KJ131).

摘　　要：朱文余和孙琦(见《数学进展》,2004,33(4):505-507)提出了关于3阶Carmichael数的三个问题,我们(见《四川大学学报(自然科学版)》,2006,43(6):1197-1201)肯定地回答了问题1.本文模仿Howe的寻找严格2阶Carmichael数(见Mathematics of Computation,2000,69(232):1711-1719)的方法,提出寻找满足某种条件的3阶Carmichael数的方法,并用这种方法确实找到了几百个这样的数,因而完全肯定地回答了问题2.ZHU and SUN [Advances in Mathematics, 33：4 （2004）, 505-507] posed three questions on Carmichael numbers of order 3. We IJournal of Sichuan University （Natural Science Edition）, 43：6 （2006）, 1197-1201] answered Question 1 affirmatively. In this paper, we answer Question 2 affirmatively by presenting a method for finding examples of Carmichael numbers of order 3 satisfying certain conditions and using the method to provide hundreds of such examples. Our method is an analog to Howe＇s one for finding rigid Carmichael numbers of order 2 [Mathematics Of Computation, 69：232（2000）, 1711-1719].

关 键 词：k阶Carmichael数 严格k阶Carmichael数 不可约多项式 

分 类 号：O156.2[理学—数学]