Problem 326

Does there exist $A=\{a_1<a_2<\cdots\}\subset \mathbb{N}$ which is a minimal basis of order $2$ (i.e. every large integer is the sum of $2$ elements from $A$ , and no proper subset of $A$ has this property), such that

\lim_{k\to \infty}\frac{a_k}{k^2}=c

for some $c\neq 0$ ?

Source: erdosproblems.com/326

Number theory
Additive bases

Wiki page

Status

ClaimedProved

A full solution has been claimed but not yet accepted. The statement is true.

Claimed: the site's label is OPEN (page last edited 2026-04-17), and the standing derives from one pending full claim: Bhalla's minimal basis with $a_k\sim ck^2$ , a manuscript of 2026-05-20 with a Lean formalization posted on 2026-06-14, not built or audited in this corpus.

Problem 326

Status

Proof claims

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