Biquadratic equations over p-adic fields
In this paper, we study a bi-quadratic equation x^4 + ax^2 = b over p-adic fields Q_p. It is worth of mentioning that the bi-quadratic equation x^4 + 1 = 0 is not solvable in the real number field R. However, the same bi-quadratic equation x^4 + 1 = 0 is solvable some p-adic fields such as p = 17,...
| Main Authors: | , |
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| Format: | Proceeding Paper |
| Language: | English |
| Published: |
2014
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| Subjects: | |
| Online Access: | http://irep.iium.edu.my/39875/ http://irep.iium.edu.my/39875/1/Biquadratic_Equation_--_IREP.pdf |
| _version_ | 1848781859359555584 |
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| author | Saburov, Mansoor Ahmad, Mohd Ali Khameini |
| author_facet | Saburov, Mansoor Ahmad, Mohd Ali Khameini |
| author_sort | Saburov, Mansoor |
| building | IIUM Repository |
| collection | Online Access |
| description | In this paper, we study a bi-quadratic equation x^4 + ax^2 = b over p-adic fields Q_p. It is worth of
mentioning that the bi-quadratic equation x^4 + 1 = 0 is not solvable in the real number field R. However,
the same bi-quadratic equation x^4 + 1 = 0 is solvable some p-adic fields such as p = 17, 41, ... Therefore, it is of independent interest to provide a solvability criterion of a bi-quadratic equation over p-adic fields. In this paper, we shall provide a solvability criterion of bi-quadratic equations in terms of a,b. |
| first_indexed | 2025-11-14T15:56:15Z |
| format | Proceeding Paper |
| id | iium-39875 |
| institution | International Islamic University Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-14T15:56:15Z |
| publishDate | 2014 |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | iium-398752018-06-18T15:21:30Z http://irep.iium.edu.my/39875/ Biquadratic equations over p-adic fields Saburov, Mansoor Ahmad, Mohd Ali Khameini QA Mathematics In this paper, we study a bi-quadratic equation x^4 + ax^2 = b over p-adic fields Q_p. It is worth of mentioning that the bi-quadratic equation x^4 + 1 = 0 is not solvable in the real number field R. However, the same bi-quadratic equation x^4 + 1 = 0 is solvable some p-adic fields such as p = 17, 41, ... Therefore, it is of independent interest to provide a solvability criterion of a bi-quadratic equation over p-adic fields. In this paper, we shall provide a solvability criterion of bi-quadratic equations in terms of a,b. 2014-09-23 Proceeding Paper PeerReviewed application/pdf en http://irep.iium.edu.my/39875/1/Biquadratic_Equation_--_IREP.pdf Saburov, Mansoor and Ahmad, Mohd Ali Khameini (2014) Biquadratic equations over p-adic fields. In: 3rd International Conference on Mathematical Applications in Engineering (ICMAE'14), 23-25 Sep 2014, Kuala Lumpur. (Unpublished) http://www.iium.edu.my/icmae/14/ |
| spellingShingle | QA Mathematics Saburov, Mansoor Ahmad, Mohd Ali Khameini Biquadratic equations over p-adic fields |
| title | Biquadratic equations over p-adic fields |
| title_full | Biquadratic equations over p-adic fields |
| title_fullStr | Biquadratic equations over p-adic fields |
| title_full_unstemmed | Biquadratic equations over p-adic fields |
| title_short | Biquadratic equations over p-adic fields |
| title_sort | biquadratic equations over p-adic fields |
| topic | QA Mathematics |
| url | http://irep.iium.edu.my/39875/ http://irep.iium.edu.my/39875/ http://irep.iium.edu.my/39875/1/Biquadratic_Equation_--_IREP.pdf |