广义Fermat数与伪素数

Generalized Fermat Numbers and Pseudoprimes

设m是正整数,b是正偶数,Gm=bbm+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≤bm1-1。

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.