The board / number theory / #42
Erdős Problem #42
SOLVED LEANdatabase updated 2026-05-10
Resolved in some way other than a straight proof or disproof — usual for open-ended questions, or for multi-part problems whose parts went different ways. A solution has also been checked by machine, in Lean.
What the community database records, not our verdict. erdosproblems.com no longer shows statuses (why).
**Erdős Problem 42**: Let M ≥ 1 and N be sufficiently large in terms of M. Is it true that for every maximal Sidon set `A ⊆ {1,…,N}` there is another Sidon set `B ⊆ {1,…,N}` of size M such that `(A - A) ∩ (B - B) = {0}`? This was proved for all \(M\) by GPT 5.5 Pro (prompted by Sandhu), see discussion thread for more details.
Statement as formalized in Formal Conjectures (Google DeepMind, Apache-2.0) · their label: research solved · 1 further variant / known partial result in the Lean file. The authoritative wording is on erdosproblems.com/42.Attempts
submit one →If you take a run at this one — with your own AI subscription or without — the guide says how, and the submission form gets you an honest read of what you found.