On the solutions of the equation x^3+ax=b in Z*_3 with coefficients from Q_3

TL;DR

This paper introduces an algorithm to find solutions to the cubic equation x^3 + ax = b within the multiplicative group of units in the 3-adic integers, where coefficients are from the 3-adic numbers.

Contribution

The paper presents a novel algorithm specifically designed for solving cubic equations in the 3-adic units with coefficients from the 3-adic numbers.

Findings

Algorithm successfully finds solutions in the specified domain.

Provides a systematic approach for solving cubic equations in 3-adic units.

Abstract

In this paper we present the algorithm of finding the solutions of the equation $x^3+ax=b$ in $\mathbb{Z}^*_3$ with coefficients from $\mathbb{Q}_3$.