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arXiv · 2108.06804

On a question of Mend\`es France on normal numbers

Verónica Becher·Manfred G. Madritsch
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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.

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Verónica Becher, Manfred G. Madritsch. 2021-08-15. On a question of Mend\`es France on normal numbers. https://arxiv.org/abs/2108.06804

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