Some Series And Congruences

In this paper, we will mainly study some special series, and study the congruent prop-erties of their partial summations. And we obtain some beautiful results. At the same time, we are also going to introduce some softwares to deal with some problems, especially how to use Maple to prove some equalities, even that they are not so obvious. At last, we study Fp[x] and put forward a question similar with Lehmer’s conjecture over Fp[x]. And we have given some partial consequences.