中文摘要：

利用映射的不动点以及不动点阶的思想将整数环Z上的Fermat小定理推广到一般集合S上，并运用该推广讨论了Dirichlet定理的一种特殊情形：只要给定正整数m≥3，那么算术数列1＋lm（l=0，1，2，…）中一定存在无穷多个素数．

英文摘要：

In this paper, the Fermat little theorem is generalized from the integer ring Z to an ordinary set S using the methods of the fixed point and its order of a map. Aapplying this generalization, the Dirichlet theorem is dis- cussed and an elementary proof is given to show that whenever m≥3, then there exit infinite primes in sequence 1 ＋ lm（l= 0,1,2,%……）, which is a special case of the Diriehlet theorem.