Sur le développement de \(\sqrt{m}\) en fraction continue p-adique. (On the expansion of \(\sqrt{m}\) in a p-adic continued fraction)
type: Item
instance of: scholarly article
title: Sur le développement de \(\sqrt{m}\) en fraction continue p-adique. (On the expansion of \(\sqrt{m}\) in a p-adic continued fraction)
zbMATH Open document ID: 0732.11068
DOI: 10.1007/BF02568429
author: Edmondo Bedocchi
published in: Manuscripta Mathematica
publication date: 1990-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/155496
review text: The Mahler-Browkin p-adic continued fraction admits partial quotients \(a/p^ b\) with \(a\in {\mathbb{Z}}\) and \(-p^{b+1}/2<a\leq p^{b+1}/2\). The author demonstrates that there are only finitely many \(m\in {\mathbb{Z}}\) so that the p-adic continued fraction expansion of \(\sqrt{m}\in {\mathbb{Q}}_ p\) is periodic with period of odd given length.
Mathematics Subject Classification ID: 11S85
Mathematics Subject Classification ID: 11J70
Mathematics Subject Classification ID: 11J61
zbMATH DE Number: 4210284
zbMATH Keywords: p-adic continued fraction expansion
MaRDI profile type: Publication
cites work: Note on \(p\)-adic continued fractions
cites work: Q3478492
cites work: Q4154643
cites work: Q4756906
cites work: Q3211400
cites work: Approximation lattices of \(p\)-adic numbers
cites work: Periodicity of \(p\)-adic continued fractions
description: scientific article; zbMATH DE number 4210284