On equation $x^q=a$ over $\bq_p$
Farrukh Mukhamedov, Mansoor Saburov
TL;DR
This paper establishes a criterion to determine when the equation x^q = a has solutions in the p-adic numbers for any natural q, advancing understanding of polynomial equations over local fields.
Contribution
It introduces a general solvability criterion for monomial equations over the field of p-adic numbers, extending previous results to all natural exponents q.
Findings
Provides a necessary and sufficient condition for solvability.
Extends previous work to arbitrary natural q.
Enhances understanding of polynomial equations over Q_p.
Abstract
In this paper we provide a solvability criterion for the monomial equation over for any natural number .
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