Solvability and number of roots of bi-quadratic equations over p−adic fields

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

	PDF (Article) - Published Version Restricted to Repository staff only Download (747kB) | Request a copy
	PDF (SCOPUS) Restricted to Repository staff only Download (168kB) | Request a copy

Abstract

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.

Item Type:	Article (Journal)
Additional Information:	6769/51131 Special Issue: The 3 rd International Conference on Mathematical Applications in Engineering 2014 (ICMAE’14)
Uncontrolled Keywords:	Bi-quadratic equation, p−adic number, solvability criterion
Subjects:	Q Science > QA Mathematics
Kulliyyahs/Centres/Divisions/Institutes (Can select more than one option. Press CONTROL button):	Kulliyyah of Science > Department of Computational and Theoretical Sciences
Depositing User:	Dr Mansoor Saburov
Date Deposited:	24 Jun 2016 10:26
Last Modified:	21 Mar 2017 19:08
URI:	http://irep.iium.edu.my/id/eprint/51131

Actions (login required)

View Item