Back to Search
Start Over
On a question of Mendès France on normal numbers
On a question of Mendès France on normal numbers
- Source :
- Acta Arithmetica. 203:271-288
- Publication Year :
- 2022
- Publisher :
- Institute of Mathematics, Polish Academy of Sciences, 2022.
-
Abstract
- In 2008 or earlier, Michel Mend\`es 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.<br />Comment: 15 pages. arXiv admin note: text overlap with arXiv:1704.03622
Details
- ISSN :
- 17306264 and 00651036
- Volume :
- 203
- Database :
- OpenAIRE
- Journal :
- Acta Arithmetica
- Accession number :
- edsair.doi.dedup.....6011ffa2a25d96a3789603a24dfc5660
- Full Text :
- https://doi.org/10.4064/aa210813-28-1