Problem 757

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Statement. Let $A\subset \mathbb{R}$ be a set of size $n$ such that every subset $B\subseteq A$ with $\lvert B\rvert =4$ has $\lvert B-B\rvert\geq 11$. Find the best constant $c>0$ such that $A$ must always contain a Sidon set of size $\geq cn$.

Status. Open.

Source. erdosproblems.com/757, accessed 2026-09-04. Cite as: T. F. Bloom, Erdős Problem #757, https://www.erdosproblems.com/757.

References.

• [GyLe95] Gyárfás, András and Lehel, Jenő, Linear sets with five distinct differences among any four elements. J. Combin. Theory Ser. B (1995), 108-118.
• [MaTa26] J. Ma and Q. Tang, Largest Sidon subsets in weak Sidon sets. arXiv:2602.23282 (2026).

Formalization. Statement in formal-conjectures.

Progress

Not yet compiled.

Known Results

Not yet compiled.

Linked library material

These entries are derived from explicit links on library pages. They are navigation only and do not by themselves record mathematical progress.

• ma_2026_largest_sidon_subsets_weak_sidon_sets
• ma_2026_largest_sidon_subsets_weak_sidon_sets / theorem_1_5
• ma_2026_largest_sidon_subsets_weak_sidon_sets / theorem_1_6