Solvability of cubic equations in p-ADIC integers (p > 3)

F. M. Mukhamedov, B. A. Omirov, M. Kh Saburov, K. K. Masutova

Research output: Contribution to journalArticlepeer-review

19 Citations (Scopus)

Abstract

We give a criterion for the existence of solutions to an equation of the form x 3 + ax = b, where a, b ∈ ℚp, in p-adic integers for p > 3. Moreover, in the case when the equation x 3 + ax = b is solvable, we give necessary and sufficient recurrent conditions on a p-adic number x ∈ ℤ*p under which x is a solution to the equation.

Original languageEnglish
Pages (from-to)501-516
Number of pages16
JournalSiberian Mathematical Journal
Volume54
Issue number3
DOIs
Publication statusPublished - May 2013
Externally publishedYes

Keywords

  • algorithm
  • cubic equation
  • p-adic number
  • solution

ASJC Scopus subject areas

  • General Mathematics

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