Open AccessThe study on general cubic equations over p-adic fields
Author(s) -
Mansoor Saburov,
Mohd Ahmad Ali,
Мурат Алп
Publication year - 2021
Publication title -
filomat
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 34
eISSN - 2406-0933
pISSN - 0354-5180
DOI - 10.2298/fil2104115s
Subject(s) - mathematics , diophantine equation , cubic function , polynomial , algebraic number field , degree (music) , field (mathematics) , pure mathematics , mathematical analysis , combinatorics , physics , acoustics
A Diophantine problem means to find all solutions of an equation or system of equations in integers, rational numbers, or sometimes more general number rings. The most frequently asked question is whether a root of a polynomial equation with coefficients in a p-adic field Qp belongs to domains Z*p, Zp \ Z*p, Qp \ Zp, Qp or not. This question is open even for lower degree polynomial equations. In this paper, this problem is studied for cubic equations in a general form. The solvability criteria and the number of roots of the general cubic equation over the mentioned domains are provided.