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陈永高的两个猜想
  • ISSN号：1000-8314
  • 期刊名称：数学年刊A辑(中文版)
  • 时间：0
  • 页码：177-182
  • 语言：中文
  • 分类：O156.1[理学—数学;理学—基础数学]
  • 作者机构：[1]南京师范大学数学与计算机科学学院,南京210097, [2]淮海工学院数理系,江苏连云港222005
  • 相关基金：国家自然科学基金（No.10771103,No.10801075）资助的项目.致谢衷心感谢陈永高教授的宝贵指导和帮助,衷心感谢审稿人提出的宝贵的修改意见.
  • 相关项目：Erdos问题、二次数域及其它数论问题
作者： 孙学功|
关键词： Chen猜想, 渐近密度, 同余覆盖系, Chen＇s conjectures, Asymptotic density, Covering systems
中文摘要：

证明了陈永高提出了下面的两个猜想是正确的：（1）设n为正整数，p为奇素数，则能够表为2^n-P形式的正整数在正奇整数的全体中有正的下渐近密度；（2）设n为正整数，p为奇素数，则能够表为P-2^n形式的正整数在正奇整数集合中有正的下渐近密度．

英文摘要：

Recently, Chen Yonggao posed the two following conjectures： （1） the set of positive odd numbers which can be expressed in the form 2^n - p has a positive lower asymptotic density in the set of all positive odd numbers; （2） the set of positive odd numbers which can be expressed in the form p - 2^n has a positive lower asymptotic density in the set of all positive odd numbers; where n is a positive integer and p is an odd prime. This paper proves that the answers to the above Chen＇s conjectures are affirmative.

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期刊信息
  • 《数学年刊：A辑》
  • 中国科技核心期刊
  • 主管单位:国家教育部
  • 主办单位:复旦大学
  • 主编：李大潜
  • 地址：上海市长乐路746号
  • 邮编：200040
  • 邮箱：edcam@fudan.edu.cn
  • 电话：021-65642338
  • 国际标准刊号：ISSN：1000-8314
  • 国内统一刊号：ISSN：31-1328/O1
  • 邮发代号:4-298
  • 获奖情况:
  • 国内外数据库收录:
  • 俄罗斯文摘杂志,美国数学评论（网络版）,德国数学文摘,中国中国科技核心期刊,中国北大核心期刊（2004版）,中国北大核心期刊（2008版）,中国北大核心期刊（2011版）,中国北大核心期刊（2014版）,中国北大核心期刊（2000版）
  • 被引量:4264