Problem Statement
Given any infinite set $A\subset \mathbb{N}$ there is a set $B$ of density $0$ such that $A+B$ contains all except finitely many integers.
Categories:
Number Theory Additive Basis
Progress
Conjectured by Erdős and Straus. Proved by Lorentz [Lo54].Source: erdosproblems.com/31 | Last verified: January 13, 2026