$P$-adic monomial equations and their perturbation

TL;DR

This paper characterizes all solutions to monomial equations over p-adic numbers and explores their perturbations, providing insights into p-adic algebraic structures and solution stability.

Contribution

It offers a complete description of solutions to monomial equations over dic fields and analyzes the effects of perturbations on these solutions.

Findings

Explicit solution sets for x^k=a over dic numbers

Analysis of solution stability under perturbations

Applications to p-adic algebraic equations

Abstract

In this paper, we describe the set of all solutions of monomial equation $x^k=a$ over $\mathbb Q_p$. Moreover, as an application of the result, we study several perturbations of the considered equation over $p$-adic field.