On equation xq = a over Qp

Farrukh Mukhamedov; Mansoor Saburov

doi:10.1016/j.jnt.2012.07.006

On equation x^q = a over Q_p

Farrukh Mukhamedov
, Mansoor Saburov

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

35 Citations (Scopus)

Abstract

In this paper we provide a solvability criterion for the monomial equation x^q = a over Qp for any natural number q. As an application of the result, we describe a relationship between q and p in which the number -1 is the q-th power of some p-adic number.

Original language	English
Pages (from-to)	55-58
Number of pages	4
Journal	Journal of Number Theory
Volume	133
Issue number	1
DOIs	https://doi.org/10.1016/j.jnt.2012.07.006
Publication status	Published - Jan 2013
Externally published	Yes

Keywords

Monomial equation
P-adic number
Solvability criterion

ASJC Scopus subject areas

Algebra and Number Theory

Access to Document

10.1016/j.jnt.2012.07.006

Cite this

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title = "On equation xq = a over Qp",

abstract = "In this paper we provide a solvability criterion for the monomial equation xq = a over Qp for any natural number q. As an application of the result, we describe a relationship between q and p in which the number -1 is the q-th power of some p-adic number.",

keywords = "Monomial equation, P-adic number, Solvability criterion",

author = "Farrukh Mukhamedov and Mansoor Saburov",

note = "Funding Information: The authors wish to express their gratitude to an anonymous referee for several helpful comments concerning a nice and compact presentation of the paper. The present study has been done within IIUM Endowment grant EDW A12-621-1412. A part of this work was done at the Abdus Salam International Center for Theoretical Physics (ICTP), Trieste, Italy. The first author thanks the ICTP for providing financial support during his visit as a Junior Associate at the centre.",

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KW - P-adic number

KW - Solvability criterion

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