p进制中幂的数字和

On the Sum of Digits of A Power in the Scal of p

给出ｐ 进制中正整数α的数字和Ｓ（α）与αｎ 的数字和Ｓ（αｎ）之间的关系：Ｓ（αｎ）－ １αｎ－ １ ≤Ｓ（α）－ １α－ １ （α≠１）．

Let p be a prime, and α,n be positive integers. Denote by S(α) the sum of digits of α in the scale of p . In this paper we prove the following result: S(α n)-1α n-1≤S(α)-1α-1(α≠1).