The board / number theory / #379
Erdős Problem #379
PROVED LEANdatabase updated 2025-08-31
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 \(S(n)\) denote the largest integer such that, for all \(1 ≤ k < n\), the binomial coefficient \(\binom{n}{k}\) is divisible by \(p^S(n)\) for some prime \(p\) (depending on \(k\)).Then \(\limsup S(n) = \infty\). This was formalized in Lean by Tao.
Statement as formalized in Formal Conjectures (Google DeepMind, Apache-2.0) · their label: research solved. The authoritative wording is on erdosproblems.com/379.Prizenone
Statement in LeanFormal Conjectures
Solution in Leanyes
Original pageerdosproblems.com/379
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.