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

International Islamic University Malaysia
National University of Uzbekistan named after Mirzo Ulugbek

Research output: Contribution to journal › Article › peer-review

21 Scopus citations

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
State	Published - May 2013
Externally published	Yes

Keywords

algorithm
cubic equation
p-adic number
solution

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10.1134/S0037446613030154

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title = "Solvability of cubic equations in p-ADIC integers (p > 3)",

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.",

keywords = "algorithm, cubic equation, p-adic number, solution",

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AU - Mukhamedov, F. M.

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AU - Saburov, M. Kh

AU - Masutova, K. K.

PY - 2013/5

Y1 - 2013/5

N2 - 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.

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

UR - https://www.scopus.com/pages/publications/84881038496

U2 - 10.1134/S0037446613030154

DO - 10.1134/S0037446613030154

M3 - 文章

AN - SCOPUS:84881038496

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VL - 54

SP - 501

EP - 516

JO - Siberian Mathematical Journal

JF - Siberian Mathematical Journal

IS - 3

ER -

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

Abstract

Keywords

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