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Erdős problem 699

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Erdős Problem 699. Is it true that for every 1≤i<j≤n/21 \le i < j \le n / 2 there exists a prime p≥ip \ge i with p∣gcd⁡((ni),(nj))p \mid \gcd\big(\binom{n}{i}, \binom{n}{j}\big)?

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699.lean

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Erdős Problem 699. Is it true that for every 1≤i<j≤n/21 \le i < j \le n / 2 there exists a prime p≥ip \ge i with p∣gcd⁡((ni),(nj))p \mid \gcd\big(\binom{n}{i}, \binom{n}{j}\big)?

FormalConjectures/ErdosProblems/699.leanErdos699.erdos_6991 lineExact file
True ↔ ∀ (n i j : ℕ), 1 ≤ i → i < j → j ≤ n / 2 → ∃ p, Nat.Prime p ∧ i ≤ p ∧ p ∣ (n.choose i).gcd (n.choose j)
OpenStatement only, no proof