Erdős Problem #1189
Erdős problem #1189 · erdosproblems.com/1189
For irreducible covering sets of size , determine their count, the possible largest modulus, the maximal reciprocal sum, and whether divisor-set examples occur infinitely often.
- Result
- Proved(see note)
- Status
- Partial result
- AI contribution
- AI-discovered
- Method
- Argument
- Field
- Number Theory, Covering Systems
- Posed by
- —
- Year posed
- —
- Years open
- —
- Solved
- 2026-07-13
- Model
- GPT-5.6 Star Fleet (Claude Fable 5 referee)
- Vendor
- OpenAI / Anthropic
- Collaborators
- —
- Verification
- Lean-verified
- Publication
- Announced
- Significance
- 10 / 100
- Disclosed cost
- —
- Wikipedia
- No dedicated article
What was actually shown
exact largest modulus 3·2^{k-3} for k ≥ 5, near-linear least maximum, reciprocal mass Θ(log k), and an infinite divisor family; the counting asymptotic rests on the cited BBMST theorem
Verification
Lean-checked with one named literature input made explicit; community status pending.