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Continued fractions in local fields, II
Authors:Jerzy Browkin.
Affiliation:Institute of Mathematics, University of Warsaw, ul. Banacha 2, PL--02--097 Warsaw, Poland
Abstract:

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 $m,$ $1<m<5000, 5nmid m$ 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 $p.$

Keywords:$p$-adic continued fractions   periodicity
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