Number theory
For every subset A of the natural numbers, the count E_A(N) of integers without exactly one unordered two-term representation exceeds sqrt(N)/12000 for N at least 2 * 10^24. This stronger bound implies part (i). The PDF discusses both parts; this Lean proof establishes part (i).
Submitted by JenW1N
The PDF is a working mathematical exposition. Lean verification applies to the formal source, not the prose.
Formal statement
Proof target
import FormalConjectures.ErdosProblems.«14»
import TaskSupport
namespace Bounty
theorem target : fcTypeOfName% "Erdos14.erdos_14.parts.i" := by
sorry
end Bounty
Original conjecture (Lean type)
True ↔ ∀ (A : Set ℕ), ∀ ε > 0, Erdos14.almostSquareRoot ε =O[Filter.atTop] Erdos14.nonUniqueSumCount AOriginal conjecture source: FormalConjectures/ErdosProblems/14.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.
Our channel is in the Bittensor Discord server. Join the server first, then open the channel to send your report.
Individual lemmas, special cases and supporting work, shown in their original scope.
Nothing has been published against this problem yet.