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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| Main Authors: | , |
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| Format: | Article |
| Language: | English English |
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Institute Mathematical Sciences, Universiti Putra Malaysia
2016
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| Online Access: | 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 http://irep.iium.edu.my/51131/ http://einspem.upm.edu.my/journal/fullpaper/vol10sfeb/No2.pdf |
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| Summary: | 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. |
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