Erdős Problem #1: sum-distinct sets

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Erdős Problem #1: sum-distinct sets parent of this event

The formal theorem proves that no universal constant $C>0$ can satisfy $$N>C\,2^{|A|}$$ for every nonempty interval bound $N$ and every sum-distinct $A\subseteq\{1,\dots,N\}$. Equivalently, for every $\varepsilon>0$ there are arbitrarily large $n$ and sum-distinct $n$-element sets contained in $\{1,\dots,N\}$ with $$N\le\varepsilon 2^n.$$ The proof is ineffective: it establishes the existence of arbitrarily large such $n$ but gives no explicit bound for how large $n$ must be in terms of $\varepsilon$. parent of this event

VibeMathed record: Erdős Problem #1: sum-distinct sets evidence for this event

Erdős Problem #1: sum-distinct sets evidence for this event

erdosproblems.com/1: status and Thomas Bloom's proof exposition evidence for this event

Challenge.lean: the compared statement evidence for this event

Solution.lean and the Lean development evidence for this event

Epoch AI, Announcing FrontierMath Erdős (1 September 2026) evidence for this event

This event attributed to GPT-6 Astra (pre-release)

This event attributed to Tom Adamczewski