@article{c4ee33f14aee40d281ace00c57295689,
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.",
year = "2013",
month = jan,
doi = "10.1016/j.jnt.2012.07.006",
language = "English",
volume = "133",
pages = "55--58",
journal = "Journal of Number Theory",
issn = "0022-314X",
publisher = "Academic Press Inc.",
number = "1",
}