Erdős Problem #7
Erdős problem #7 · erdosproblems.com/7
Can there be a finite covering system of the integers with distinct moduli, all of which are odd and greater than ?
- Result
- Proved
- Status
- Retracted
- AI contribution
- —
- Method
- Argument
- Field
- Number Theory, Covering Systems
- Posed by
- —
- Year posed
- —
- Years open
- —
- Solved
- 2026-05-07
- Model
- Aristotle
- Vendor
- Harmonic
- Collaborators
- —
- Verification
- Contested
- Publication
- Announced
- Significance
- 10 / 100
- Disclosed cost
- —
- Wikipedia
- No dedicated article
What the AI did
Both the failed formalization and the audit that exposed its false axiom were AI-assisted.
Verification
Claim withdrawn; see the claim issue. Recorded because failed formalizations are part of the honest history of AI mathematics.
Claim issue
The claimed Lean proof that no such covering system exists was withdrawn after audit: its central axiom asserted that a product of factors greater than one is less than one, and a statement-fidelity audit confirmed the gap. The problem remains open.