A stronger connection between the Erdős-Burgess and Davenport constants

Abstract

The Erdős-Burgess constant of a semigroup S is the smallest positive integer k such that any sequence over S of length k contains a nonempty subsequence whose terms multiply to an idempotent element of S. In the case where S is the multiplicative semigroup of Z/nZ, we confirm a conjecture connecting the Erdős-Burgess constant of S and the Davenport constant of (Z/nZ)× for n with at most two prime factors. We also discuss the extension of our techniques to other rings.