Erdős problem 1 · problems.science

If $A\subseteq\{1, ..., N\}$ with $|A| = n$ is such that the subset sums $\sum_{a\in S}a$ are distinct for all $S\subseteq A$ then $N \gg 2 ^ n.$

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8 retained statements2415f78e850a

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FormalConjectures/ErdosProblems/

1.lean

Retained formal statement3 of 8

A number of improvements of the constant $\frac{1}{4}$ have been given, with the current record $\sqrt{2 / \pi}$ first provided in unpublished work of Elkies and Gleason.

FormalConjectures/ErdosProblems/1.leanErdos1.erdos_1.variants.lb_strong3 linesExact file

1∃ o,2  ∃ (_ : o =o[Filter.atTop] 1),3    ∀ (N : ℕ) (A : Finset ℕ), Erdos1.IsSumDistinctSet A N → (√(2 / Real.pi) - o A.card) * 2 ^ A.card / √↑A.card ≤ ↑N

SolvedStatement only, no proof

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