方幂和中奇素数因子P的指数问题

THE EXPONENT OF ODD PRIME FACTOR P IN POWER SUM

设ｎ，ｘ，ｒ为正整数且ｒ＞１，ｐ为奇素数，ｎ＝ｐαｃ，ｐｃ，本文给出下面一类方幂和中因子ｐ的指数计算公式，并给出其在不定方程中一个应用：Ｄ＝∑ｎ－１ｋ＝０（ｘ＋ｄｋ）ｒ，ｄ＝ｐｓ＋１。

Let n,x,r be positive integer with r>1,p be odd prime,n=pc,pc,the exponent of factor p in power sum:D=Σn-1k=0(x+dk)r,d=ps+1,s≥0 is discussed and a calculation formula and an example are given.