Problem 434

Let $k\leq n$ . What choice of $A\subseteq \{1,\ldots,n\}$ (with $\mathrm{gcd}(A)=1$ ) of size $\lvert A\rvert=k$ maximises the number of integers not representable as the sum of finitely many elements from $A$ (with repetitions allowed)? Is it $\{n,n-1,\ldots,n-k+1\}$ ?

Source: erdosproblems.com/434

Number theory

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An accepted solution exists. The statement is true.

PROVED (LEAN): the site's label; its commentary credits Kiss with the proof, and the frontmatter standing is derived from the accepted claim page Kiss's theorem, accepted on the site's credit and the journal publication; the Lean part of the label refers to a separate AI-assisted Lean proof arguing from Dixmier's theorem, recorded as the claimed page Lean proof through Dixmier's interval theorem, which this corpus has not built or audited.

Problem 434

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