Arithmetic Progressions in a Unique Factorization Domain
  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. 
Sudhir R. Ghorpade and Samrith Ram
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