The board / number theory / #433
Erdős Problem #433
PROVED LEANdatabase updated 2026-02-24
The statement as posed is true, and a proof exists. 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).
The Frobenius number of a finite set \(A\): the greatest natural number outside the additive submonoid generated by \(A\).
The largest Frobenius number of a \(k\)-element subset of \(\{1,\ldots,n\}\) whose elements have greatest common divisor one.
For every fixed \(k \geq 2\), Erdős and Graham conjectured that \[g(k,n) \sim \frac{n^2}{k-1}.\] The conjecture was proved by Dixmier [Di90].
Statement as formalized in Formal Conjectures (Google DeepMind, Apache-2.0) · their label: research solved. The authoritative wording is on erdosproblems.com/433.Prizenone
Topicsnumber theory
Statement in LeanFormal Conjectures
Solution in Leanyes
Original pageerdosproblems.com/433
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.