erdos_699

Specification

**Erdős Problem 699.** Is it true that for every $1 \le i < j \le n / 2$ there exists a prime $p \ge i$ with $p \mid \gcd\big(\binom{n}{i}, \binom{n}{j}\big)$?

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Lean 4 Statement

theorem erdos_699 : answer(sorry) ↔
    ∀ n i j : ℕ,
      1 ≤ i →
      i < j →
      j ≤ n / 2 →
      ∃ p : ℕ, p.Prime ∧ i ≤ p ∧ p ∣ Nat.gcd (Nat.choose n i) (Nat.choose n j)

ID: ErdosProblems__699__erdos_699

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