一篇数学论文。讨论了数论中关于幂指式同余的周期性问题，给出了最小正周期的表达式和几个关于幂指式同余周期的性质。为快速构造或化简同余幂指式提供了一般方法。对研究密码学，尤其是讨论RSA公钥密码体制有一定参考价值。-A mathematical papers. Discussed for a number of means on the power-type with more than a cyclical problem, given the smallest cycle is the expression of and a few on the power-type congruence refers to the nature of cycles. For the rapid construction or congruence of Jane style refers to power provided a general approach. The study of cryptography, especially the discussion of RSA public-key cryptosystem has a certain reference value.