Erdős Problem #868

The problem

If $A$ is an additive basis of order $2$, and $1_A\ast 1_A(n)\to \infty$ as $n\to \infty$, then must $A$ contain a minimal additive basis of order $2$? (i.e. such that deleting any element creates infinitely many $n\not\in A+A$)

What if $1_A\ast 1_A(n) >\epsilon \log n$ (for all large $n$, for arbitrary fixed $\epsilon>0$)?

Statement quoted from erdosproblems.com/868, maintained by Thomas Bloom. Original source: [ErNa79][Er92c]. Current status there: solved (Lean).

AI contributions

As recorded in Terence Tao's wiki AI contributions to Erdős problems (data as of 30 Jun 2026). 🟢 full, 🟡 partial, ⚪ unverified, 🔴 incorrect.

Caveats

The wiki's classifications are provisional and are not a benchmark. Many Erdős problems have never had a thorough literature review, so a result that looks new may later turn out to be known; some problems were also stated ambiguously or incorrectly. See the problem page for the full discussion.

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