Gauss's proof of the irreducibility of the p-th cyclotomic polynomial

Time: 6:00-8:00pm

Location: Mendel 103, Villanova University

Abstract: The irreducibility of the cyclotomic polynomials is a basic result in number theory. There is a well-known and easy proof irreducibility of the p-th cyclotomic polynomial, for p a prime, due to Schoenemann/Eisenstein (1846/1850). But this result was first proved by Gauss in the Disquisitiones Arithmeticae. We present Gauss's beautiful and intricate proof. Not only is this proof interesting in itself, it also sheds light on what was and was not common knowledge among mathematicians of the day.