Solvable Sextic Equations

TL;DR

This paper provides criteria to determine when an irreducible sextic polynomial with rational coefficients can be solved algebraically over the complex numbers.

Contribution

It introduces specific criteria for solvability of irreducible sextic equations, advancing understanding of polynomial solvability.

Findings

Criteria for algebraic solvability of sextic equations

Conditions for irreducibility over rationals

Implications for solving complex sextic equations

Abstract

Criteria are given for determining whether an irreducible sextic equation with rational coefficients is algebraically solvable over the complex numbers.