等幂和的性质  

Properties of the Sum of Equal Power Series

作　　者：施俊[1] 彭庆英 

机构地区：[1]江苏理工学院数理学院,江苏常州213001 [2]江苏省常州技师学院,江苏常州213018

出　　处：《江苏理工学院学报》2016年第4期7-11,共5页Journal of Jiangsu University of Technology

基　　金：国家自然科学青年基金资助项目(11501257);江苏理工学院面上项目(KYY14012)

摘　　要：首先讨论了等幂和的整除性,利用二项式展开定理及帕斯卡等式得出了等幂和的几个组合性质.然后,利用费马小定理、原根等工具研究了受限等幂和模奇素数的次幂的同余性质,并推广到非受限等幂和,得出几个非常漂亮的同余性质。The divisibility of the sum of equal power series are discussed by using the Binomial expansion theorem and Pascal＇ s identity, derived some combinatorial properties of the sum of equal power series. By Fermat＇ s little theorem and the primitive root etc., it studied congruence properties of restricted power sums modulo odd prime powers（i.e.）, furthermore, congruence properties also hold to unrestricted power sums, moreover, some other wonderful results are also obtained.

关 键 词：等幂和 整除性 组合性 同余性 

分 类 号：O156.4[理学—数学]