Arithmetic progressions in a unique factorization domain
Arithmetic progressions in a unique factorization domain
Sudhir R. Ghorpade
Department of Mathematics
Indian Institute of Technology Bombay
Powai, Mumbai 400076, India
E-Mail: srg@math.iitb.ac.in
and
Samrith Ram
Department of Mathematics
Indian Institute of Technology Bombay
Powai, Mumbai 400076, India
E-Mail: samrith@gmail.com
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.
1 | Introduction | 1 |
2 | Arithmetic progressions of integers | 2 |
3 | GCD domains and decomposition numbers | 6 |
4 | Arithmetic progressions in GCD domains | 8 |
| References | 11 |
This paper is published in Acta Arithmetica, Vol. 54, No. 2 (2012), pp. 161-171.
[Preprint Version:
arXiv.math/1108.1267v1 (August 2011)]
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