费马数是合数的一个充要条件

A Sufficient and Necessary Condition of the Proposition that the Fermat Numbers are Composite

文章运用数论中的一些简单结果,如(F_m,F_n)=1及F_n=2^(2^n)+1(n≥2)的素因数p具有形状p=2^(n+2)k+1,其中k为某正整数等,给出了费马数是合数的一个充要条件,并得到了F_5,F_6和F_7的素因数分解式。

In this paper, we give a sufficient and necessary condition of the proposition that the Fermat number are composite, by using the simple result among the number theory, for instance, （ Fm, Fn） = 1 and suppose thatp is a prime divisor of Fn = 2^2＊ ＋ 1 （ n≥2） ,then it is of the fromp = 2^n＋2 k ＋ 1, where k is a positive integer. We also obtain the prime factorization of F5, F6 and F7 .