Problem #109: Any $A\subseteq \mathbb{N}$ of positive upper density...

Any $A\subseteq \mathbb{N}$ of positive upper density contains a sumset $B+C$ where both $B$ and $C$ are infinite.

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Problem Statement

Any $A\subseteq \mathbb{N}$ of positive upper density contains a sumset $B+C$ where both $B$ and $C$ are infinite.

Categories: Additive Combinatorics

The Erdős sumset conjecture. Proved by Moreira, Richter, and Robertson [MRR19].

See also [656].

Source: erdosproblems.com/109 | Last verified: January 13, 2026