The board / number theory / #727
Erdős Problem #727
OPENdatabase updated 2025-08-31
No proof or disproof is known, and it isn't known whether a finite computation could settle it.
What the community database records, not our verdict. erdosproblems.com no longer shows statuses (why).
Let \(k ≥ 2\). Does \(((n+k)!)^2∣(2n)!\) hold for infinitely many \(n\)?
Statement as formalized in Formal Conjectures (Google DeepMind, Apache-2.0) · their label: research open · 3 further variants / known partial results in the Lean file. The authoritative wording is on erdosproblems.com/727.Prizenone
Topicsnumber theory, factorials
Statement in LeanFormal Conjectures
Solution in Leanno
Original pageerdosproblems.com/727
Attempts
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Live page status OPEN with 0 claimed proofs, but “Currently working on this problem” lists ryin and boolean_matrix (accessed 2026-07-28); stopped before mathematics to avoid colliding with current wor
SKIPPED