Additive combinatoricsReadingErdős problem #757
Erdős and Sós; bounds last moved in February 2026
- Best known
- c ≤ 4/7 ≈ 0.5714, from a 14-number set (Ma and Tang, 2026)
- Proven limit
- c ≥ 9/17 ≈ 0.5294, proven (Ma and Tang, 2026)
- Target
- one finite set whose largest Sidon subset is below 4/7 of its size
- Progress
- No result yet.
erdosproblems.com/757
Dense polynomials, sparse squares
Rényi and Erdős, 1947; upper bound unchanged since 1949
- Best known
- about n^0.811 terms (Verdenius, 1949)
- Proven limit
- at least a constant times log n (Schinzel and Zannier, 2009)
- Target
- a polynomial whose square has fewer than √n terms; any family below n^0.811
- Progress
- No result yet.
Epoch AI, FrontierMath Open Problems