Erdős Problem #684
Prior state unknown→proved
For the least $k$ at which the small-prime part of $\binom{n}{k}$ exceeds $n^2$, how large can $f(n)$ be?
SourceReplayReproducedFormal proofStatement auditExternal checkExpert reviewPeer review! Disputed
number-theory / Number Theory, Binomial Coefficients
Erdős Problem #684
For the least $k$ at which the small-prime part of $\binom{n}{k}$ exceeds $n^2$, how large can $f(n)$ be?
10Significance / 100
1Frontier events
0Verification tasks
0Recorded attempts
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For the least $k$ at which the small-prime part of $\binom{n}{k}$ exceeds $n^2$, how large can $f(n)$ be?
A preprint claimed $\limsup f(n)/\log n = \infty$, but a deterministic audit later found a counterexample to its key Lemma 18. The stated conclusion is not established and the problem remains open.
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