关于费马解的一个同余方程

On the Congruent Equation of the Fermat Solution

设p为奇素数,a为整数,若ap-1≡(1mod p2),则a名为费马解。根据华罗庚给出的几个特殊的费马解,可以探求费马解的一般方法。利用初等方法及原根的性质研究同余方程xp-1≡(1modpl),l≥1的可解性,可以得到该同余方程的一切正整数解和费马解。

Ifap-1≡（1modp2）（p is an odd prime and a is a integer）, a is called me rermat sore tion. According to the several special Fermat solutions Hua Luo-geng provided, the general methods for Fermat solutions can be found. And if the elementary method and the properties of the primitive roots are used to study the solvability of the congruent equation xpp-1≡（1modpl）,l≥1 all the positive integer solutions and Fermat solutions will be obtained.