XXIV.—Sets of Integers Containing not more than a Given Number of Terms in Arithmetical Progression
XXIV.—Sets of Integers Containing not more than a Given Number of Terms in Arithmetical Progression
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XXIV.——算术级数中包含不超过给定数量项的整数集
DOI：
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发表时间：
1961
期刊：
影响因子：
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通讯作者：
R. Rankin
中科院分区：
文献类型：
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作者：
R. Rankin
整数的集合被构造成具有这样的性质，即只有当n个成员都相等时，它们才是算术级数;这里n是大于或等于3的任何整数。先前的结果仅在n=3时获得。这个问题可以用不同的方法来概括。该分析也可用于构造类似的几何级数问题的集合。这些集合是正密度的，不像第一类集合，它们的密度为零。
SYNOPSIS Sets of integers are constructed having the property that n members are in arithmetical progression only if they are all equal; here n is any integer greater than or equal to 3. Previous results have been obtained only for n=3. The problem is generalized in various ways. The analysis can also be applied to construct sets for the analogous problem of geometrical progressions. These sets are of positive density, unlike those of the first kind, which have zero density.