关于正规数的一个Mendès France问题
On a question of Mendès France on normal numbers
摘要：
在2008年或更早的时候，Michel Mendès France要求一个实数$x$的实例，使得$x$和$1/x$对于给定的整数基$b$都是简单正规的。通过构造一个数$x$，使得$x$及其倒数$1/x$都是连分数正规的，并且对于所有大于或等于$2$的整数基都是正规的，我们给出了一个肯定的答案.此外，$x$和$1/x$都是可计算的。
英文摘要：
In 2008 or earlier, Michel Mendès France asked for an instance of a real number $x$ such that both $x$ and $1/x$ are simply normal to a given integer base $b$. We give a positive answer to this question by constructing a number $x$ such that both $x$ and its reciprocal $1/x$ are continued fraction normal as well as normal to all integer bases greater than or equal to $2$. Moreover, $x$ and $1/x$ are both computable.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
