Erdős problem 698 · problems.science

Is there some $h(n)\to \infty$ such that for all $2\leq i<j\leq n/2$ $\textrm{gcd}\left( \binom{n}{i},\binom{n}{j}\right) \geq h(n)?$

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FormalConjectures/ErdosProblems/

698.lean

Retained formal statement4 of 4

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

FormalConjectures/ErdosProblems/698.leanErdos698.erdos_698.variants.erdos_szekeres_sharp5 linesExact file

1∀ (p : ℕ),2  Nat.Prime p →3    2 < p →4      ↑(((2 * p).choose 1).gcd ((2 * p).choose p)) = ↑((2 * p).choose 1) / ↑(p.choose 1) ∧5        ↑((2 * p).choose 1) / ↑(p.choose 1) = 2 ^ 1

SolvedStatement only, no proof

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