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.
Combinatorics
Date added
Green's open problem 15
Does there exist a Lipschitz function f:N→Z whose graph
Γ={(n,f(n)):n∈N}⊆Z2
is free of 3-term progressions?
$2,640 bounty·nobody has started
week of 18 Sept 2025 · nothing publishedweek of 25 Sept 2025 · nothing publishedweek of 2 Oct 2025 · nothing publishedweek of 9 Oct 2025 · nothing publishedweek of 16 Oct 2025 · nothing publishedweek of 23 Oct 2025 · nothing published
Solve it
Nobody has attempted this. A complete proof or refutation takes the whole bounty.
18 Sept 2025nothing published against this one yet10 Sept 2026
[Gr24] Green, Ben. "100 open problems." (2024).
[BJP14] T. Brown, V. Jungić and A. Poelstra, "On double 3-term arithmetic progressions", Integers 14 (2014), Paper No. A43.
[CCS14] J. Cassaigne, J. D. Currie, L. Schaeffer and J. Shallit, "Avoidance of additive cubes and related results", Adv. in Appl. Math. 56 (2014), 25–66.
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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