等幂和的末位数字及其分解性质  

Last Digits of Sum of Equal Powers and Their Decomposition Properties

作　　者：王云葵[1] 

机构地区：[1]广西民族学院数学与计算机科学系,南宁市大学路530006

出　　处：《广西科学》2003年第1期4-7,共4页Guangxi Sciences

基　　金：广西民族学院重点科研项目资助(02SXX00001)。

摘　　要：设p为奇素数,αn为等幂和表成2p进制的末位数字,获得等幂和的同余性与等幂和的周期性,从而证明当p-1×m时,αn是最小正周期为4p的周期数列;当p-1│m时,αn是最小正周期为4p2的周期数列,并且完全确定当等幂和表成10进制时的末位数字αn,等幂和的数论性质对G.Giuga猜想等研究有着重要的作用.Let p be odd prime number, an be last digits of sum of equal powers at 2p system. The coresidual property and periodicity of sum of equal powers are obtained. It is proved that an is periodic numeral series of minimum positive period of 4p when p - 1×m, and periodic numeral series of minimum positive period of 4 p2 when p - 1│m. The last digits of sum of equal powers at decimal system are determined. The sum of equal powers plays an important role in the study of Giuga guess.

关 键 词：等幂和 周期性 末位数字 降幂公式 奇偶性 

分 类 号：O156[理学—数学]