On cubic equations over p-adic fields

Farrukh Mukhamedov, Bakhrom Omirov, Mansoor Saburov

Research output: Contribution to journalArticlepeer-review

23 Citations (Scopus)

Abstract

We provide a solvability criterion for a cubic equation in domains Z p, Zp, Qp. We show that, in principal, the Cardano method is not always applicable for such equations. Moreover, the numbers of solutions of the cubic equation in domains Zp, Z p, Qp are provided. Since p is a subgroup of p, we generalize Serre's and Sun's results concerning with cubic equations over the finite field p. Finally, all cubic equations, for which the Cardano method could be applied, are described and the p-adic Cardano formula is provided for those cubic equations.

Original languageEnglish
Pages (from-to)1171-1190
Number of pages20
JournalInternational Journal of Number Theory
Volume10
Issue number5
DOIs
Publication statusPublished - Aug 2014
Externally publishedYes

Keywords

  • Cubic equation
  • p-adic Cardano formula
  • p-adic number
  • solvability criterion

ASJC Scopus subject areas

  • Algebra and Number Theory

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