The board / number theory / #392
Erdős Problem #392
PROVED LEANdatabase updated 2026-02-22
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).
Let \(A(n)\) denote the least value of \(t\) such that \[ n! = a_1 \cdots a_t \] with \(a_1 \leq \cdots \leq a_t\leq n^2\). Then \[ A(n) = \frac{n}{2} - \frac{n}{2\log n} + o\left(\frac{n}{\log n}\right). \]
Statement as formalized in Formal Conjectures (Google DeepMind, Apache-2.0) · their label: research solved · 2 further variants / known partial results in the Lean file. The authoritative wording is on erdosproblems.com/392.Prizenone
Topicsnumber theory, factorials
Statement in LeanFormal Conjectures
Solution in Leanyes
Original pageerdosproblems.com/392
Attempts
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