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.
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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 |
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International Islamic University Malaysia |
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English |
topic |
QA Mathematics |
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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 |
_version_ |
1777409230057242624 |