2026/07/19 by Wen Huang, Zhengxing Lian, Song Shao +3
Mathematics · #math.CO #math.DS #math.NT
In the newest version, we resolve the weighted form of Owings's sumset question completely
arxiv created 2026/07/29 · arxiv updated 2026/07/30
We give an affirmative answer to Owings's sumset question: for any 2-coloring of natural numbers, there is an infinite B⊆ℕ such that B+B is monochromatic. More generally, for every m,ℓ∈ℕ and every 2-coloring of ℕ, there is an infinite B⊆ℕ such that (m+ℓ)B∪\mx+ℓ y:x,y∈ B, x<y\ is monochromatic.