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

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

doi:10.1134/S0037446613030154

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 journal › Article › peer-review

20 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 ∈ ℚ_p, 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 language	English
Pages (from-to)	501-516
Number of pages	16
Journal	Siberian Mathematical Journal
Volume	54
Issue number	3
DOIs	https://doi.org/10.1134/S0037446613030154
Publication status	Published - May 2013
Externally published	Yes

Keywords

algorithm
cubic equation
p-adic number
solution

ASJC Scopus subject areas

General Mathematics

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10.1134/S0037446613030154

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PY - 2013/5

Y1 - 2013/5

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AB - 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.

KW - algorithm

KW - cubic equation

KW - p-adic number

KW - solution

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JF - Siberian Mathematical Journal

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

Abstract

Keywords

ASJC Scopus subject areas

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