关于整数和集的定理的推广  

About Popularization of Theorem of Sumset of Integers

作　　者：陈雪生[1] 唐明军[1] 

机构地区：[1]中南大学数学科学与计算技术学院,长沙410075

出　　处：《数学理论与应用》2009年第1期81-84,共4页Mathematical Theory and Applications

摘　　要：本文主要利用加性数论的理论考察整数和集,推广了VsevolodF.Lev的关于整数和的定理:设n≥1,B■[1,n],|B|>4n,k=|B|+1,则(1)当1≤n≤2k-3时,有ias能写成两个不同B中元之和。(2)当2k-2≤n<3k-3时,有ias能写成最多四个B中元之和。(3)当3k-3≤n<4k-4时,有ias能写成最多2h个B中元之和。其中h=max[4k-24k-n],i=1,2,3,4。This paper mainly use additive number theory to investigate sumset of integers. We spread Vsevolod F. Lev＇ s theorem about sumset of integers as follwing： Let n≥1,B lohtain in [1,n], ｜ B｜ 〉n/4,k= ｜ B｜ ＋ 1,then （1）when 1 ≤n≤2k- 3,there exist two dements of B whose sum is ia^s （2）when 2k- 2≤n〈 3k- 3,there exist at most four dements of B whose stun is ia^s （3）when 3k - 3 ≤ n 〈 4k - 4, there exist at most 2 h dements of B whose sum is ia^s where h= max[2k/4k-4-n] ,i = 1,2,3,4,6

关 键 词：整数和集 整数的幂 正规型 

分 类 号：O156[理学—数学]