| 孙学功.陈永高的两个猜想[J].数学年刊A辑,2009,30(2):177~182 |
| 陈永高的两个猜想 |
| On Two Conjectures of Chen Yonggao |
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| DOI： |
| 中文关键词: Chen猜想 渐近密度 同余覆盖系 |
| 英文关键词:Chen’s conjectures, Asymptotic density, Covering systems |
| 基金项目:国家自然科学基金 |
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| 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2n-p形式的正整数在正奇整数的伞体中有正的F渐近密度; (2)设n为正整数,p为奇素数,则能够表为p-2n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 2n?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 ? 2n 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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