论文标题
ERDS原始套装的证明
A proof of the Erdős primitive set conjecture
论文作者
论文摘要
如果集合中没有成员除另一个成员，则一组大于1的整数是原始的。 Erdő在1935年证明了$ f（a）= \ sum_ {a \ in} 1/（a \ log a）$在原始集合$ a $的所有选择上均匀地界定。 1986年，他询问是否为一组质数获得了这种界限。在本文中，我们回答了肯定。随着该方法的进一步应用，我们从1968年开始朝着Erdős，Sárközy和Szemerédi的问题取得了进展。我们还完善了经典的Davenport-Erdőstheorem关于无限划分链的定理，并扩展了Erdős，Sárközy和Szemerédi的结果。
A set of integers greater than 1 is primitive if no member in the set divides another. Erdős proved in 1935 that the series $f(A) = \sum_{a\in A}1/(a \log a)$ is uniformly bounded over all choices of primitive sets $A$. In 1986 he asked if this bound is attained for the set of prime numbers. In this article we answer in the affirmative. As further applications of the method, we make progress towards a question of Erdős, Sárközy, and Szemerédi from 1968. We also refine the classical Davenport-Erdős theorem on infinite divisibility chains, and extend a result of Erdős, Sárközy, and Szemerédi from 1966.
