Number theory
No subset of the natural numbers has o(sqrt(N)) exceptions to unique unordered two-term representation. The PDF discusses both parts; this Lean proof refutes the possibility proposed in part (ii).
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.ii" := by
sorry
end Bounty
Original conjecture (Lean type)
True ↔ ∃ A, Erdos14.nonUniqueSumCount A =o[Filter.atTop] Erdos14.squareRootOriginal 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.
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Individual lemmas, special cases and supporting work, shown in their original scope.
Nothing has been published against this problem yet.