On equation x^q=a over Q_p

In this paper we provide a solvability criterion for the monomial equation x^q = a over Qp for any natural number q. As an application of the result, we describe a relationship between q and p in which the number −1 is the q-th power of some p-adic number.

Bibliographic Details
Main Authors: Mukhamedov, Farrukh, Saburov, Mansoor
Format: Article
Language:English
Published: Academic Press Inc. 2013
Subjects:
Online Access:http://irep.iium.edu.my/26067/
http://irep.iium.edu.my/26067/
http://irep.iium.edu.my/26067/
http://irep.iium.edu.my/26067/1/mfms-JNT%282012%29.pdf
id iium-26067
recordtype eprints
spelling iium-260672012-12-14T06:06:26Z http://irep.iium.edu.my/26067/ On equation x^q=a over Q_p Mukhamedov, Farrukh Saburov, Mansoor QA Mathematics In this paper we provide a solvability criterion for the monomial equation x^q = a over Qp for any natural number q. As an application of the result, we describe a relationship between q and p in which the number −1 is the q-th power of some p-adic number. Academic Press Inc. 2013-01 Article PeerReviewed application/pdf en http://irep.iium.edu.my/26067/1/mfms-JNT%282012%29.pdf Mukhamedov, Farrukh and Saburov, Mansoor (2013) On equation x^q=a over Q_p. Journal of Number Theory, 133 (1). pp. 55-58. ISSN 0022-314X (P), 1096-1658 (O) http://dx.doi.org/10.1016/j.jnt.2012.07.006 10.1016/j.jnt.2012.07.006
repository_type Digital Repository
institution_category Local University
institution International Islamic University Malaysia
building IIUM Repository
collection Online Access
language English
topic QA Mathematics
spellingShingle QA Mathematics
Mukhamedov, Farrukh
Saburov, Mansoor
On equation x^q=a over Q_p
description In this paper we provide a solvability criterion for the monomial equation x^q = a over Qp for any natural number q. As an application of the result, we describe a relationship between q and p in which the number −1 is the q-th power of some p-adic number.
format Article
author Mukhamedov, Farrukh
Saburov, Mansoor
author_facet Mukhamedov, Farrukh
Saburov, Mansoor
author_sort Mukhamedov, Farrukh
title On equation x^q=a over Q_p
title_short On equation x^q=a over Q_p
title_full On equation x^q=a over Q_p
title_fullStr On equation x^q=a over Q_p
title_full_unstemmed On equation x^q=a over Q_p
title_sort on equation x^q=a over q_p
publisher Academic Press Inc.
publishDate 2013
url http://irep.iium.edu.my/26067/
http://irep.iium.edu.my/26067/
http://irep.iium.edu.my/26067/
http://irep.iium.edu.my/26067/1/mfms-JNT%282012%29.pdf
first_indexed 2023-09-18T20:38:52Z
last_indexed 2023-09-18T20:38:52Z
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