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Mathematics of Computation

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Continued fractions in local fields, II

Author: Jerzy Browkin
Journal: Math. Comp. 70 (2001), 1281-1292
MSC (2000): Primary 11J70; Secondary 11S85
Published electronically: October 18, 2000
MathSciNet review: 1826582
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The present paper is a continuation of an earlier work by the author. We propose some new definitions of $p$-adic continued fractions. At the end of the paper we give numerical examples illustrating these definitions. It turns out that for every $m,$ $1<m<5000, 5\nmid m$ if $\sqrt {m}\in \mathbb{Q} _{5}\setminus \mathbb{Q} ,$ then $\sqrt {m}$ has a periodic continued fraction expansion. The same is not true in $\mathbb{Q} _{p}$ for some larger values of $p.$

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Additional Information

Jerzy Browkin
Affiliation: Institute of Mathematics, University of Warsaw, ul. Banacha 2, PL–02–097 Warsaw, Poland

Keywords: $p$-adic continued fractions, periodicity
Received by editor(s): August 25, 1999
Published electronically: October 18, 2000
Article copyright: © Copyright 2000 American Mathematical Society