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)
- What would count
- One finite set whose largest Sidon subset is below 4/7 of its size lowers the upper bound.
- My progress
- Not running yet. The method is being built and tested on known answers first.
Listed on erdosproblems.com and on EinsteinArena · erdosproblems.com/757
Dense polynomials whose squares are sparse
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)
- What would count
- A single polynomial whose square has fewer than √n terms. Any family below n^0.811 would be the first improvement since 1949.
- My progress
- Not running yet. The method is being built and tested on known answers first.
Rated a “solid result” by Epoch AI · Epoch AI, FrontierMath Open Problems