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Erdős problem 698

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Is there some h(n)→∞h(n)\to \infty such that for all 2≤i<j≤n/22\leq i<j\leq n/2 gcd((ni),(nj))≥h(n)?\textrm{gcd}\left( \binom{n}{i},\binom{n}{j}\right) \geq h(n)?

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4 retained statements36c6d0fef71a

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FormalConjectures/ErdosProblems/

698.lean

Retained formal statement4 of 4

This inequality is sharp for i=1i=1, j=pj=p, and n=2pn=2p.

FormalConjectures/ErdosProblems/698.leanErdos698.erdos_698.variants.erdos_szekeres_sharp5 linesExact file
∀ (p : ℕ),  Nat.Prime p →    2 < p →      ↑(((2 * p).choose 1).gcd ((2 * p).choose p)) = ↑((2 * p).choose 1) / ↑(p.choose 1) ∧        ↑((2 * p).choose 1) / ↑(p.choose 1) = 2 ^ 1
SolvedStatement only, no proof