Arithmetic Progressions in a Unique Factorization Domain

Details Arithmetic Progressions in a Unique Factorization Domain Arithmetic Progressions in a Unique Factorization Domain

2011-08-05

arxiv.org/abs/1108.1267v2

Mathematics

Number Theory

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

Scientific paper

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.

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