On the greatest common divisor of shifted sets

Randell Heyman*, Igor E. Shparlinski

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

Given a set of n positive integers {a1, ..., an} and an integer parameter H we study the greatest common divisor of small additive shifts of its elements by integers hi with |hi| ≤ H, i = 1, ..., n. In particular, we show that for any choice of a1, ..., an there are shifts of this type for which the greatest common divisor of a1 + h1, ..., an+hn is much larger than H.

Original languageEnglish
Pages (from-to)63-73
Number of pages11
JournalJournal of Number Theory
Volume154
DOIs
Publication statusPublished - 1 Sep 2015
Externally publishedYes

Keywords

  • Approximate GCD
  • GCD

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