Solvability and number of roots of bi-quadratic equations over p−adic fields
Unlike the real number field R, a bi-quadratic equation x4 + 1 = 0 is solvable over some p−adic number fields Qp, say p = 17, 41, · · · . Therefore, it is of independent interest to provide a solvability criterion for the bi-quadratic equation over p−adic number fields Qp. In this paper, we provide...
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Institute Mathematical Sciences, Universiti Putra Malaysia
2016
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| Online Access: | http://irep.iium.edu.my/51131/ http://irep.iium.edu.my/51131/1/Bi-Quadratic_Eq_---_MJMS.pdf http://irep.iium.edu.my/51131/4/51131-Solvability%20and%20number%20of%20roots%20of%20bi-quadratic%20equations%20over%20p-adic%20fields_SCOPUS.pdf |
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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 | Unlike the real number field R, a bi-quadratic equation x4 + 1 = 0 is solvable over some p−adic number fields Qp, say p = 17, 41, · · · . Therefore, it is of independent interest to provide a solvability criterion for the bi-quadratic equation over p−adic number fields Qp. In this paper, we provide solvability criteria for the bi-quadratic equation x4 + ax2 = b over domains Z ∗ p, Zp \ Z ∗ p, Qp \ Zp, Qp, where p > 2. Moreover, we also provide the number of roots of the bi-quadratic equation over the mentioned domains. |
| first_indexed | 2025-11-14T16:26:57Z |
| format | Article |
| id | iium-51131 |
| institution | International Islamic University Malaysia |
| institution_category | Local University |
| language | English English |
| last_indexed | 2025-11-14T16:26:57Z |
| publishDate | 2016 |
| publisher | Institute Mathematical Sciences, Universiti Putra Malaysia |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | iium-511312017-03-21T11:08:11Z http://irep.iium.edu.my/51131/ Solvability and number of roots of bi-quadratic equations over p−adic fields Saburov, Mansoor Ahmad, Mohd Ali Khameini QA Mathematics Unlike the real number field R, a bi-quadratic equation x4 + 1 = 0 is solvable over some p−adic number fields Qp, say p = 17, 41, · · · . Therefore, it is of independent interest to provide a solvability criterion for the bi-quadratic equation over p−adic number fields Qp. In this paper, we provide solvability criteria for the bi-quadratic equation x4 + ax2 = b over domains Z ∗ p, Zp \ Z ∗ p, Qp \ Zp, Qp, where p > 2. Moreover, we also provide the number of roots of the bi-quadratic equation over the mentioned domains. Institute Mathematical Sciences, Universiti Putra Malaysia 2016-02 Article PeerReviewed application/pdf en http://irep.iium.edu.my/51131/1/Bi-Quadratic_Eq_---_MJMS.pdf application/pdf en http://irep.iium.edu.my/51131/4/51131-Solvability%20and%20number%20of%20roots%20of%20bi-quadratic%20equations%20over%20p-adic%20fields_SCOPUS.pdf Saburov, Mansoor and Ahmad, Mohd Ali Khameini (2016) Solvability and number of roots of bi-quadratic equations over p−adic fields. Malaysian Journal of Mathematical Sciences, 10 (S) (Part 1). pp. 15-35. ISSN 1823-8343 http://einspem.upm.edu.my/journal/fullpaper/vol10sfeb/No2.pdf |
| spellingShingle | QA Mathematics Saburov, Mansoor Ahmad, Mohd Ali Khameini Solvability and number of roots of bi-quadratic equations over p−adic fields |
| title | Solvability and number of roots of bi-quadratic equations over p−adic fields |
| title_full | Solvability and number of roots of bi-quadratic equations over p−adic fields |
| title_fullStr | Solvability and number of roots of bi-quadratic equations over p−adic fields |
| title_full_unstemmed | Solvability and number of roots of bi-quadratic equations over p−adic fields |
| title_short | Solvability and number of roots of bi-quadratic equations over p−adic fields |
| title_sort | solvability and number of roots of bi-quadratic equations over p−adic fields |
| topic | QA Mathematics |
| url | http://irep.iium.edu.my/51131/ http://irep.iium.edu.my/51131/ http://irep.iium.edu.my/51131/1/Bi-Quadratic_Eq_---_MJMS.pdf http://irep.iium.edu.my/51131/4/51131-Solvability%20and%20number%20of%20roots%20of%20bi-quadratic%20equations%20over%20p-adic%20fields_SCOPUS.pdf |