有限循环群中的零和问题  

On the zero-sum of the finite cyclic group

作　　者：魏贵民[1] 齐丽丽[1] 钟锐[1] 

机构地区：[1]成都理工大学信息管理学院,成都610059

出　　处：《成都理工大学学报（自然科学版）》2008年第2期210-211,共2页Journal of Chengdu University of Technology: Science & Technology Edition

摘　　要：设n是大于1的正整数,p是n的最小素因子。记X是以Zn中元素为元素,长度为n+k的序列,其中k≥n/p-1。该文证明了当n只有两个不同素因子时,如果Zn中的每个元素在X中至多重复k次,则X中必然存在一个长度为n的子序列,它的元素之和为零。从而给出了W.D.Gao猜想成立的一种情况。Let n〉l be a positive integer and p the smallest prime divisor of n. Let X be a sequence of elements from ￡n of length n＋k, where k≥n /p-1. If every element of ￡n, appears in X at most k times, this paper proves that there must be a subsequence of X of length n whose sum is zero when n has only two different prime divisors. So the W. D. Gao conjecture is true when n= p^αq^β, where p, q are distinct primes and α, β are positive intergers.

关 键 词：序列 子集 有限循环群 零和 

分 类 号：O152.1[理学—数学]