Number theory
$4,996 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-975Command 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.«975»
import TaskSupport
namespace Bounty
theorem target : fcTypeOfName% "Erdos975.erdos_975" := by
sorry
end Bounty
Original conjecture (Lean type)
True ↔
∀ (f : Polynomial ℤ),
f.natDegree ≠ 0 →
Irreducible f →
(∀ᶠ (n : ℤ) in Filter.atTop, 1 ≤ Polynomial.eval n f) →
∃ c > 0, Filter.Tendsto (fun x => Erdos975.Erdos975Sum f x / (x * Real.log x)) Filter.atTop (nhds c)Original conjecture source: FormalConjectures/ErdosProblems/975.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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