费马数与伪素数

Fermat Number and Pseudoprime Number

如果合数N满足2N≡2(modN),则称N为伪素数.本文运用数论中的一些简单结果,如任何费马合数都是伪素数以及费马小定理(若p为素数,a为整数,且(a,p)=1,则ap-1≡1(modp))等,给出了N=FS1FS2…FSk为伪素数的充要条件:S1≤2S2-1且SSk,FSi=22Si+1为费马数。

If a composite number N satisfies 2N≡2（modN）,then N is called Pseudoprime number.In this paper,by using the simple result among the number theory,as every Fermat composite number is a Pseudoprime number and Fermat＇s Little Theorem（If p is prime and a is a positive integer with（a,p）=1,then ap-1≡1（modp） etc,we give a sufficient and necessary condition of the proposition that N=FS1FS2…FSkis a pseudoprime number,it is S1≤2S2-1 and Sk≤2S1-1,where S1S2…Sk and FSi=22Si＋1 is Fermat number.