Arithmetic Progressions in a Unique Factorization Domain
Number Theory
2013-05-31 v2 Rings and Algebras
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.
Cite
@article{arxiv.1108.1267,
title = {Arithmetic Progressions in a Unique Factorization Domain},
author = {Sudhir R. Ghorpade and Samrith Ram},
journal= {arXiv preprint arXiv:1108.1267},
year = {2013}
}
Comments
Version 2 (to appear in Acta Arithmetica) with minor typos corrected