Number theory
Approved
For every positive epsilon, h(n!) is eventually smaller than n^epsilon. This establishes the factorial target in part (b); it is separate from the question about general practical integers in part (a).
Submitted by JenW1N
Formal statement
Proof target
import Mathlib
import FormalConjectures.ErdosProblems.«18»
import TaskSupport
namespace Bounty
theorem target : fcTypeOfName% "Erdos18.erdos_18b" := by
sorry
end Bounty
Original conjecture (Lean type)
True ↔ ∀ (ε : ℝ), 0 < ε → ∀ᶠ (n : ℕ) in Filter.atTop, ↑(Erdos18.practicalH n.factorial) < ↑n ^ εOriginal conjecture source: FormalConjectures/ErdosProblems/18.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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Individual lemmas, special cases and supporting work, shown in their original scope.
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conjectures-tasks
The pinned statement, the Lean challenge file and the exact bundle you build against.
versions/fc-v2-erdos18-erdos-18b-88242fe05d6de992dee0af8e-formalized →
conjectures-contribution
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contributions/erdos-18-b →