Arithmetic progressions in a unique factorization domain (Q2893039)

The generalized Pillai theorem states that in any set of at most 16 consecutive integers in arithmetic progression, there exists an integer that is relatively prime to all the rest. Here the authors are interested in the analogue of this result to arbitrary integral domains where the notion of greatest common divisor makes sense.NEWLINENEWLINEThe main result is an analogue of the generalized Pillai theorem for the so-called \(\sigma\)-atomic GCD domains of characteristic zero and in particular, for arbitrary unique factorization domains of characteristic zero. E.g., the generalized Pillai theorem holds for the Gaussian integers with 16 replaced by 6.