OPENHARDnumber theoryadditive combinatorics
If $A\subseteq \{1,\ldots,N\}$ with $|A|=n$ is such that the subset sums $\sum_{a\in S}a$ are distinct for all $S\subseteq A$ then $N \gg 2^{n}$.
Notes: Erdos and Moser proved N >= (1/4 - o(1)) * 2^n / sqrt(n). Dubroff, Fox, and Xu proved the exact bound N >= C(n, floor(n/2)). Powers of 2 show that 2^n would be optimal.
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