[1]杨仕椿,汤建钢.Sárközy的一个加法剩余类问题[J].南京师范大学学报(自然科学版),2013,36(02):10-14.
 Yang Shichun,Tang Jiangang.A Problem on the Addition of Residue Classes by Sárközy[J].Journal of Nanjing Normal University(Natural Science Edition),2013,36(02):10-14.
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Sárközy的一个加法剩余类问题()
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《南京师范大学学报》(自然科学版)[ISSN:1001-4616/CN:32-1239/N]

卷:
第36卷
期数:
2013年02期
页码:
10-14
栏目:
数学
出版日期:
2013-06-30

文章信息/Info

Title:
A Problem on the Addition of Residue Classes by Sárközy
文章编号:
1001-4616(2013)02-0010-05
作者:
杨仕椿12汤建钢1
1.伊犁师范学院数学与统计学院,新疆 伊宁 835000
2.阿坝师范高等专科学校数学系,四川 汶川 623000
Author(s):
Yang Shichun12Tang Jiangang1
1.College of Mathematics and Statistics,Yili Normal University,Yining 835000,China
2.Department of Mathematics,ABa Teachers College,Wenchuan 623000,China
关键词:
加法剩余类偶数模Sárközy问题
Keywords:
additionresidue classeseven number moduloSárközy problem
分类号:
O156.1
文献标志码:
A
摘要:
关于A+B以及A+^B的性质问题,一直是数论与组合数学中的困难课题和重要问题.本文首先指出,在一般情况下,关于Sárközy的一个加法剩余类猜想的答案是否定的.其次,对于模偶数m的既约剩余系,利用Cauchy-Davenport定理,给出当m=2p,2kp(k≥2)时该问题的两个初步的结果,这里p为素数.最后,提出一些待研究的问题和猜想.
Abstract:
The characteristic of the A+B and A+^B,is a difficult topic in number theory and combinatorics,and plays an important and profound role.In this paper,we first noted that under normal circumstances,the answer of a problem on the addition of residue classes by Sárközy is negative.Secondly,for the mode even number m of irreducible residue system,using Cauchy-Davenport theorem,we give the problem in two preliminary results when m=2 p,2k p(k≥2),where p is a prime number.Finally,we presented some problems and conjectures to be studied.

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备注/Memo

备注/Memo:
收稿日期:2012-10-20.
基金项目:新疆维吾尔自治区普通高等学校重点学科经费资助项目(2012ZDXK21)、四川省科技厅应用基础研究重点项目(2011JYZ032)、四川省教育厅自然科学研究项目(12ZB002)、阿坝师专重点科研基金项目.
通讯联系人:汤建钢,教授,研究方向:不确定性的数学处理,经典与非经典计算理论,范畴论及其应用.E-mail:jg-tang@163.com
更新日期/Last Update: 2013-06-30