摘要: |
设p为奇素数,an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,an是最小正周期为4p的周期数列;当p-1│m时,an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an,等幂和的数论性质对G.Giuga猜想等研究有着重要的作用. |
关键词: 等幂和 周期性 末位数字 |
DOI: |
投稿时间:2002-06-17 |
基金项目:广西民族学院重点科研项目资助(02SXX00001)。 |
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Last Digits of Sum of Equal Powers and Their Decomposition Properties |
Wang Yunkui
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(Dept. of Mathematics and Computer Science, Guangxi University for Nationalities, Daxuelu, Nanning, Guangxi, 530006, China) |
Abstract: |
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 4p2 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. |
Key words: sum of equal powers periodicity last digit |