Erdős Problem #774
No proof or disproof is known, and it isn't known whether a finite computation could settle it.
What the community database records, not our verdict. erdosproblems.com no longer shows statuses (why).
We call \(A\subset \mathbb{N}\) dissociated if \(\sum_{n\in X}n\neq \sum_{m\in Y}m\) for all finite \(X,Y\subset A\) with \(X\neq Y\).
We call \(A\) proportionately dissociated if every finite \(B\subset A\) contains a dissociated set of size \(\gg \lvert B\rvert\). In other words, there is a (global) \(c > 0\) such that every finite \(B \subset A\) contains a dissociated set of size \(\geq c|B|\).
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exact 15-point obstruction/table and base-family classification verified; #774 remains equivalent to the unresolved uniform finite bound \(C(\delta)<\infty\).
PARTIAL