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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| Main Authors: | , |
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| Format: | Conference or Workshop Item |
| Language: | English |
| Published: |
2014
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| Subjects: | |
| Online Access: | 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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| Summary: | 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. |
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