FormalConjectures.ErdosProblems.«1094»

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import FormalConjecturesUtil

Erdős Problem 1094

Reference: erdosproblems.com/1094


namespace Erdos1094


open scoped Nat

For all $n\ge 2k$ the least prime factor of $\binom{n}{k}$ is $\le\max(n/k,k)$, with only finitely many exceptions.

@[category research open, AMS 11]
theorem declaration uses 'sorry'erdos_1094 :
    {(n, k) : ℕ × ℕ | 0 < k ∧ 2 * k ≤ n ∧ (n.choose k).minFac > max (n / k) k}.Finite := by⊢ {(n, k) | 0 < k ∧ 2 * k ≤ n ∧ (n.choose k).minFac > max (n / k) k}.Finite
  sorryAll goals completed! 🐙


end Erdos1094