Combinatorics
$5,072 bountynobody has started
Nobody has attempted this. A complete proof or refutation takes the whole bounty.
Even one lemma helps. Whoever finishes this later shares the pool with everyone who got them there.
contrib new erdos-1192Command line, then a pull request on GitHub.
Nothing has been published against this problem yet.
A first lemma is worth as much as a last one: whoever closes the problem shares the pool with everyone who got them there.
Formal statement
Proof target
import FormalConjectures.ErdosProblems.«1192»
import TaskSupport
namespace Bounty
theorem target : fcTypeOfName% "Erdos1192.erdos_1192" := by
sorry
end Bounty
Original conjecture (Lean type)
True ↔
∀ r ≥ 2,
∃ A,
(∀ᶠ (n : ℕ) in Filter.atTop, Erdos1192.f_r A r n > 0) ∧
(fun x => ∑ n ∈ Finset.range (x + 1), ↑(Erdos1192.f_r A r n) ^ 2) =O[Filter.atTop] fun x => ↑xOriginal conjecture source: FormalConjectures/ErdosProblems/1192.lean
References
Something wrong with this formalization?
A statement that does not faithfully capture the original conjecture is the one real risk here, so we would rather hear about it early - before someone spends weeks on it.
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