Every problem here was open when it entered the pool.
Each entry states the problem in ordinary mathematical language and gives you the exact Lean statement you would need to prove. Nothing is paraphrased, so what you read is what gets checked.
Number theory
Green's open problem 2
Let A⊂Z be a set of n integers. Is there a set S⊂A of size
(logn)100
[Er65] P. Erdős. Extremal problems in number theory, In Proc. Sympos. Pure Math., Vol. VIII, pages 181–189. Amer. Math. Soc., Providence, R.I., 1965.
[Sa21] Sanders, Tom. "The Erdős–Moser Sum-free Set Problem." Canadian Journal of Mathematics 73.1 (2021): 63-107.
[Ru05] I. Z. Ruzsa, Sum-avoiding subsets. Ramanujan J., 9 (2005) (1-2):77–82.
[Ch71] S. L. G. Choi. On a combinatorial problem in number theory. Proc. London Math. Soc. (3), 23:629–642, 1971. doi:10.1112/plms/s3-23.4.629.
[BSS00] A. Baltz, T. Schoen, and A. Srivastav. Probabilistic construction of small strongly sum-free sets via large Sidon sets. Colloq. Math., 86(2):171–176, 2000. doi:10.4064/cm-86-2-171-176.
No one has attempted this yet.
Formal statement
Lean type
True ↔
∀ᶠ (n : ℕ) in Filter.atTop,
∀ (A : Finset ℤ), A.card = n → ↑(Green2.maxRestrictedSumAvoidingSubsetSize A) ≥ Real.log ↑n ^ 100
What you must prove
import FormalConjectures.GreensOpenProblems.«2»
import TaskSupport
namespace Bounty
theorem target : ¬ (fcTypeOfName% "Green2.green_2") := by
sorry
end Bounty
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.