{"id":"palomar/PALOMAR-2026-11-03-000016","url":"https://github.com/veljjanoski/erdos338-palomar/tree/a699263d0f7cdce0e5b3026bce86eab30973d0f8","json":"https://data.palomar-registry.org/entries/PALOMAR-2026-11-03-000016-v1.json","repo":"https://github.com/veljjanoski/erdos338-palomar","tags":["math.NT","math.CO","msc:11B13","msc:11B05"],"score":0,"title":"Erdős Problem 338: restricted order of robust sets of positive lower density","trust":"high","domain":"math.NT","source":"palomar","authors":["Daniel Veljjanoski"],"reviews":0,"subject":"math.NT","summary":"If A \\ F is a basis for every finite set F and A has positive lower density, then A has a restricted order: every sufficiently large integer is a sum of a bounded number of distinct elements of A. This is a partial result on Erdős Problem 338 (Erdős and Graham ask whether every such A, without the density condition, has a restricted order). The proof counts pairs to show that, for every R, the numbers with at least R representations as a sum of two distinct elements of A have positive lower density, uniformly in R; uses Kneser's theorem for finite abelian groups to write all large numbers of…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"verified":true,"discussed":0,"published":"2026-11-03","reactions":{},"formalized":true,"formalizes":[{"title":"Erdős problem #338: partial results on restricted order","identifier":"","relationship":"formalizes"},{"title":"Answer to a question by Burr and Erdős on restricted addition, and related results","identifier":"","relationship":"adapts"}]}