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

关键词:  等幂和  周期性  末位数字

Key words:  sum of equal powers  periodicity  last digit

摘要:

设p为奇素数,a_n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,a_n是最小正周期为4p的周期数列;当p-1│m时,a_n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a_n,等幂和的数论性质对G.Giuga猜想等研究有着重要的作用.

Abstract:

Let p be odd prime number, a_n 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 a_n 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.