论文标题
$ \ times b $ invariant套件中的理性数字
Rational numbers in $\times b$-invariant sets
论文作者
论文摘要
令$ b \ geq 2 $是整数，而$ s $是一套有限的非空数，不包含$ b $的除数。对于任何非密集的集合$ a \ subset [0,1）$，以便在$ \ times b $操作下$ a \ cap \ mathbb {q} $是不变的，我们证明了$ a $中有理数的有限数字只能由Primes in $ s $ s $划分。还获得了$ a $的分母的最大主要分数的定量结果。
Let $b \geq 2$ be an integer and $S$ be a finite non-empty set of primes not containing divisors of $b$. For any non-dense set $A \subset [0,1)$ such that $A \cap \mathbb{Q}$ is invariant under $\times b$ operation, we prove the finiteness of rational numbers in $A$ whose denominators can only be divided by primes in $S$. A quantitative result on the largest prime divisors of the denominators of rational numbers in $A$ is also obtained.
