Erdős problem 699 · problems.science

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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3 retained statements2415f78e850a

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FormalConjectures/ErdosProblems/

699.lean

Retained formal statement2 of 3

Erdős and Szekeres conjectured that, apart from a finite exceptional set of triples (n, i, j), one can always take p > i in the prime divisor statement.

FormalConjectures/ErdosProblems/699.leanErdos699.erdos_szekeres_strengthening4 linesExact file

1True ↔2  ∃ E,3    ∀ (n i j : ℕ),4      1 ≤ i → i < j → j ≤ n / 2 → (n, i, j) ∉ E → ∃ p, Nat.Prime p ∧ i < p ∧ p ∣ (n.choose i).gcd (n.choose j)

OpenStatement only, no proof

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