An altenative proof of the Catalan conjecture

Abstract

The original proof [5] of Catalan’s conjecture uses real binomial power series expansions and annihilation of real class groups, based on a Theorem of Thaine. In this paper we provide a simplified approach to this proof, which uses Stickelberger annihilation of the minus part of the class group, and thus does not require the Theorem of Thaine. The approach is based on proving the existence of a character connecting Galois exponents of roots of unity.