Geodesic
The study on general cubic equations over p-adic fields
Filomat, Tome 35 (2021) no. 4, p. 1115

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DOI

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
DOI : 10.2298/FIL2104115S
Classification : 11D88, 11D25, 11S05
Keywords: Cubic equation, p-adic field, solvability criterion, number of roots 
Mansoor Saburov; Mohd Ali Khameini Ahmad; Murat Alp. The study on general cubic equations over p-adic fields. Filomat, Tome 35 (2021) no. 4, p. 1115 . doi: 10.2298/FIL2104115S
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     title = {The study on general cubic equations over p-adic fields},
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     pages = {1115 },
     year = {2021},
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     doi = {10.2298/FIL2104115S},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2104115S/}
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