## On simultaneous uniform approximation to a $p$-adic number and its square

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- Proc. Amer. Math. Soc.
**138**(2010), 3821-3826 Request permission

## Abstract:

Let $p$ be a prime number. We show that a result of Teulié is nearly best possible by constructing a $p$-adic number $\xi$ such that $\xi$ and $\xi ^2$ are uniformly simultaneously very well approximable by rational numbers with the same denominator. The same conclusion was previously reached by Zelo in his PhD thesis, but our approach using $p$-adic continued fractions is more direct and simpler.## References

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## Additional Information

**Yann Bugeaud**- Affiliation: Département de Mathématiques, Université de Strasbourg, 7, rue René Descartes, 67084 Strasbourg, France
- Email: bugeaud@math.unistra.fr
- Received by editor(s): January 29, 2010
- Published electronically: May 21, 2010
- Communicated by: Ken Ono
- © Copyright 2010
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc.
**138**(2010), 3821-3826 - MSC (2010): Primary 11J13, 11J61
- DOI: https://doi.org/10.1090/S0002-9939-2010-10491-4
- MathSciNet review: 2679605