Arithmetic Progressions in a Unique Factorization Domain

Abstract

Pillai showed that any sequence of consecutive integers with at most 16 terms possesses one term that is relatively prime to all the others. We give a new proof of a slight generalization of this result to arithmetic progressions of integers and further extend it to arithmetic progressions in unique factorization domains of characteristic zero.

Version 2 (to appear in Acta Arithmetica) with minor typos corrected