Erdős Problem #494

The problem

If $A\subset \mathbb{C}$ is a finite set and $k\geq 1$ then let

$$A_k = \{ z_1+\cdots+z_k : z_i\in A\textrm{ distinct}\}.$$

For $k>2$ does the multiset $A_k$ (together with the size of $A$) uniquely determine the set $A$?

Statement quoted from erdosproblems.com/494, maintained by Thomas Bloom. Original source: [Er61]. Current status there: proved.

AI contributions

As recorded in Terence Tao's wiki AI contributions to Erdős problems (data as of 30 Jun 2026). 🟢 full, 🟡 partial, ⚪ unverified, 🔴 incorrect.

Caveats

The wiki's classifications are provisional and are not a benchmark. Many Erdős problems have never had a thorough literature review, so a result that looks new may later turn out to be known; some problems were also stated ambiguously or incorrectly. See the problem page for the full discussion.

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