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,...
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2014
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my.iium.irep.39875 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 Conference or Workshop Item 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 (Unpublished) http://www.iium.edu.my/icmae/14/ |
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QA Mathematics Saburov, Mansoor Ahmad, Mohd Ali Khameini Biquadratic equations over p-adic fields |
| 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. |
| format |
Conference or Workshop Item |
| author |
Saburov, Mansoor Ahmad, Mohd Ali Khameini |
| author_facet |
Saburov, Mansoor Ahmad, Mohd Ali Khameini |
| author_sort |
Saburov, Mansoor |
| title |
Biquadratic equations over p-adic fields |
| title_short |
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_sort |
biquadratic equations over p-adic fields |
| publishDate |
2014 |
| url |
http://irep.iium.edu.my/39875/1/Biquadratic_Equation_--_IREP.pdf http://irep.iium.edu.my/39875/ http://www.iium.edu.my/icmae/14/ |
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1643616764095889408 |
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13.222552 |