一类集合的 3 因子个数研究

3-Factor Number Study of aClass of Sets

本论文研究由任意非 3 因子元素组成的集合 其中D是一无穷整数子集,我们证明了对任意的k≥1,存在无穷多个𝛾1,𝛾2∈A,它们的差𝛾1−𝛾2至少有k个 3 因子。 分别讨论了集合A是整数集或有理数集下,利用数学归纳法以及集合之间的包含关系证得了上述结论是成立的。

In this thesis, we study the set consisting of any non-3-factor element where D is an infinite subset of integers.We show that there are infinitely many 𝛾1,𝛾2∈A, and their difference 𝛾1−𝛾2 has at least 𝑘 factors of 3 for any k≥1. If A is set of integers or set of rational numbers, the above conclusion is proved by mathematical inductionand the induction relation between sets.