2017/02/08 by Alexander Fish, Fish, Alexander
Engineering · Mathematics · #Combinatorics (math.CO) #Dynamical Systems (math.DS) #FOS: Mathematics #Limits and Structures in Graph Theory #Mathematics and Applications #Number Theory (math.NT) #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.1702.02544
openalex publication_date 2017/02/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we prove that given two sets E1,E2 ⊂ ℤ of positive density, there exists k ≥ 1 which is bounded by a number depending only on the densities of E1 and E2 such that kℤ ⊂ (E1-E1)⋅(E2-E2). As a corollary of the main theorem we deduce that if α,β> 0 then there exist N0 and d0 which depend only on α and β such that for every N ≥ N0 and E1,E2 ⊂ ℤN with |E1| ≥ αN, |E2| ≥ βN there exists d ≤ d0 a divisor of N satisfying d ℤN ⊂ (E1-E1)⋅(E2-E2).