Problem 881

Let $A\subset\mathbb{N}$ be an additive basis of order $k$ which is minimal, in the sense that if $B\subset A$ is any infinite set then $A\backslash B$ is not a basis of order $k$ .

Must there exist an infinite $B\subset A$ such that $A\backslash B$ is a basis of order $k+1$ ?

Source: erdosproblems.com/881

Number theory
Additive bases

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Status

ClaimedDisproved

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

Claimed: a pending full claim answers the question no; the site's label is OPEN and the site lists no proof claim. A manuscript posted in the site's thread on 2026-05-03 claims a complete answer, no for every $k\ge2$ , and is the pending claim Svyable; a reader's AI check reports that it counts sums of exactly $k$ elements where the site's definition allows at most $k$ , and finds fatal defects in its proof.

Problem 881

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Proof claims

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