一类互不相交的整数集合

A Class of Disjoint Sets of Integers

应用几何级数、素数以及限制参数范围的方法构造了几组互不相交的整数集合,给出了它们的一般性构造表达式.用反证法和素数相关的整除性质,证明了这些集合随着参数的变化是互不相交的,然后指出了对利用偶素数构造的整数集合限制参数范围可以实现与用奇素数构造的整数集合互不相交.最后给出了所构造集合在密度问题上的一个应用.

In this paper,several sets of disjoint integer sets are constructed by using geometric series,prime numbers and restricted parameter ranges,and their general construction expressions are given.It is proved that these sets are mutually disjoint with the change of parameters by using the inverse proof method and the prime number related integer division property.Then,it is pointed out that the integer set constructed by even prime numbers can be disjoint with the integer set constructed by odd prime numbers by limiting the parameter range.Finally,an application of the constructed set in the density problem is given.