Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4593604 | Journal of Number Theory | 2015 | 11 Pages |
Abstract
Given a set of n positive integers {a1,â¦,an} and an integer parameter H we study the greatest common divisor of small additive shifts of its elements by integers hi with |hi|â¤H, i=1,â¦,n. In particular, we show that for any choice of a1,â¦,an there are shifts of this type for which the greatest common divisor of a1+h1,â¦,an+hn is much larger than H.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Randell Heyman, Igor E. Shparlinski,