Zgjidhja e ekuacionit t\"e grad\"es s\"e 5-t\"e

TL;DR

This paper investigates the solvability of irreducible quintic equations by radicals, establishing conditions based on Galois group properties and invariants, thus advancing understanding of algebraic solutions for fifth-degree polynomials.

Contribution

It provides necessary and sufficient conditions for the solvability of irreducible quintic equations using invariants and Galois theory, offering a new criterion for algebraic solvability.

Findings

Conditions for solvability expressed via invariants

Characterization of Galois group solvability for quintics

Advancement in algebraic solution criteria for fifth-degree equations

Abstract

An irreducible quintic equation is solvable by radicals if and only if its Galois group is solvable. In this work, we provide necessary and sufficient conditions for solvability, expressed in terms of invariants of the quintic.