Problem Statement
Let $\epsilon>0$. Does there exist $A\subseteq \mathbb{N}$ such that the lower density of $A+A$ is at least $1-\epsilon$ and yet $1_A\ast 1_A(n) \ll_\epsilon 1$ for all $n$?
Categories:
Additive Combinatorics
Progress
A similar question can be asked for upper density.See also [28].
Source: erdosproblems.com/749 | Last verified: January 16, 2026