On Two Conjectures of Chen Yonggao
On Two Conjectures of Chen Yonggao
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论陈永高的两个猜想
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发表时间：
2009
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最近，陈永高提出了以下两个猜想：(1)正奇数集合在所有正奇数集合中具有正下渐近密度，其可以用2~n-p的形式表示；(2)可表示为p-2~n的正奇数集合在所有正奇数集合中具有正下渐近密度；其中n是正整数p是奇素数。本文证明了上述陈氏猜想的答案是肯定的。
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.