等幂和数列的周期性

The Periodicity of the Sequence of the Sum of Equal Powers

设M为一个无平方因子正整数,an(M)为等幂和Sm(n)=1m+2m+…+nm模M的最小非负剩余.文章证明了an(M)为周期数列,并给出了这一序列的周期的计算方法.

Let M be a square-free positive integer,an（M） be the least non-negative residue of the sum of equal powers Sm（n）= 1m＋2m＋…＋nm modulo M. In this paper,we show that an（M） is a periodic sequence,and we establish a method to compute its period.