Catalog

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 \subset \mathbf{Z}

be a set of

n

integers. Is there a set

S \subset A

of size

(\log n)^{100}

such that the restricted sumset

S \hat{+} S

is disjoint from

A

References

[Gr24] Green, Ben. "100 open problems." (2024).
[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.

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Formal statement