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.
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Academic Press Inc.
2013
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| Subjects: | |
| Online Access: | http://irep.iium.edu.my/26067/ http://irep.iium.edu.my/26067/1/mfms-JNT%282012%29.pdf |
| _version_ | 1848779578297810944 |
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| author | Mukhamedov, Farrukh Saburov, Mansoor |
| author_facet | Mukhamedov, Farrukh Saburov, Mansoor |
| author_sort | Mukhamedov, Farrukh |
| building | IIUM Repository |
| collection | Online Access |
| 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. |
| first_indexed | 2025-11-14T15:20:00Z |
| format | Article |
| id | iium-26067 |
| institution | International Islamic University Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-14T15:20:00Z |
| publishDate | 2013 |
| publisher | Academic Press Inc. |
| recordtype | eprints |
| repository_type | Digital Repository |
| 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 |
| spellingShingle | QA Mathematics Mukhamedov, Farrukh Saburov, Mansoor On equation x^q=a over Q_p |
| title | 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_short | On equation x^q=a over Q_p |
| title_sort | on equation x^q=a over q_p |
| topic | QA Mathematics |
| 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 |