The board / number theory / #387
Erdős Problem #387
SOLVEDdatabase updated 2026-07-02
Resolved in some way other than a straight proof or disproof — usual for open-ended questions, or for multi-part problems whose parts went different ways.
What the community database records, not our verdict. erdosproblems.com no longer shows statuses (why).
Is there an absolute constant \(c > 0\) such that, for all \(1 \leq k < n\), the binomial coefficient \(\binom{n}{k}\) has a divisor in \((cn, n]\)? Bui, Naprienko, Pratt, and Zaharescu [BNPZ26] answered this negatively.
Statement as formalized in Formal Conjectures (Google DeepMind, Apache-2.0) · their label: research solved · 3 further variants / known partial results in the Lean file. The authoritative wording is on erdosproblems.com/387.Attempts
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