Problem Statement
Does there exist a minimal basis with positive density, say $A\subset\mathbb{N}$, such that for any $n\in A$ the (upper) density of integers which cannot be represented without using $n$ is positive?
Categories:
Number Theory Additive Basis
Progress
Asked by Erdős and Nathanson.Source: erdosproblems.com/330 | Last verified: January 14, 2026