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@archiebrowne archiebrowne commented Dec 18, 2025

Let $A \subset \mathbb{N}$ be an infinite set for which there exists some $\epsilon > 0$ such that
in any subset of $A$ of size $n$ there is a subset of size at least $\epsilon n$ which contains no
three-term arithmetic progression.

Is it true that $A$ is the union of a finite number of sets which contain no three-term arithmetic
progression?

Closes #973

@YaelDillies YaelDillies added the awaiting-author The author should answer a question or perform changes. Reply when done. label Dec 20, 2025
@YaelDillies YaelDillies changed the title Erdos 847 feat(ErdosProblems): 847 Dec 20, 2025
@Paul-Lez Paul-Lez self-requested a review January 9, 2026 11:53
Co-authored-by: Paul Lezeau <paul.lezeau@gmail.com>
@github-actions github-actions bot added the erdos-problems Erdős Problems label Jan 9, 2026
with HasFew3APs name instead of h\eps
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Done! thanks

archiebrowne and others added 2 commits January 20, 2026 08:15
Co-authored-by: Yaël Dillies <yael.dillies@gmail.com>
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Thanks!

archiebrowne and others added 2 commits January 22, 2026 09:39
Co-authored-by: Paul Lezeau <paul.lezeau@gmail.com>
Co-authored-by: Paul Lezeau <paul.lezeau@gmail.com>
@Paul-Lez Paul-Lez enabled auto-merge (squash) January 22, 2026 09:51
@Paul-Lez Paul-Lez merged commit a39f2b8 into google-deepmind:main Jan 22, 2026
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@archiebrowne archiebrowne deleted the erdos_847 branch January 22, 2026 11:40
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Erdős Problem 847

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