Problem Statement
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 $\{n,n-1,\ldots,n-k+1\}$?
Categories:
Number Theory
Progress
Associated with problems of Frobenius (see also [433]).The maximal choice is indeed $\{n,\ldots,n-k+1\}$, as proved by Kiss [Ki02].
Source: erdosproblems.com/434 | Last verified: January 15, 2026