Problem 433

If $A\subset \mathbb{N}$ is a finite set then let $G(A)$ denote the greatest integer which is not expressible as a finite sum of elements from $A$ (with repetitions allowed). Let

g(k,n)=\max G(A)

where the maximum is taken over all $A\subseteq \{1,\ldots,n\}$ of size $\lvert A\rvert=k$ which has no common divisor. Is it true that

g(k,n)\sim \frac{n^2}{k-1}?

Source: erdosproblems.com/433

Number theory

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SolvedProved

An accepted solution exists. The statement is true.

PROVED (LEAN): the site's label; its commentary credits Dixmier with the proof. The frontmatter standing is derived from the accepted claim page Dixmier's bounds, accepted on the site's credit and the refereed publication; the Lean part of the label refers to a forum-posted formalization of Dixmier's theorems, recorded on that page, which this corpus has not built or audited.

Problem 433

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Proof claims

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