A Note on Cyclotomic Polynomials

TL;DR

This paper offers a generalized proof of the irreducibility of cyclotomic polynomials over Q and specific number fields, providing new insights and conditions related to algebraic solutions by radicals.

Contribution

It introduces a new, more general proof of cyclotomic polynomial irreducibility and explores implications for algebraic solutions by radicals.

Findings

Cyclotomic polynomials are irreducible over Q and certain number fields.

Provides a necessary condition for algebraic solutions by radicals.

Connects known results with new consequences.

Abstract

We present a more general proof that cyclotomic polynomials are irreducible over Q and other number fields that meet certain conditions. The proof provides a new perspective that ties together well-known results, as well as some new consequences, including a necessary condition for the algebraic solution by radicals of certain irreducible polynomials.