This article is cited in 23 papers

$p$-adic monomial equations and their perturbations

F. M. Mukhamedov, O. N. Khakimov

United Arab Emirates University

Abstract: In this paper, we describe the set of solutions of the monomial equation $x^k=a$ over $\mathbb Q_p$. Moreover, as an application, we study some perturbations of the equation under consideration over the $p$-adic field.

Keywords: monomial equation, $p$-adic numbers, rational function.

UDC: 517.98+530.1

MSC: 37B05, 37B10, 12J12, 39A70

Received: 07.06.2018
Revised: 06.11.2018

DOI: 10.4213/im8821

 English version: Izvestiya: Mathematics, 2020, 84:2, 348–360

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