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 $p \mid \gcd\big(\binom{n}{i}, \binom{n}{j}\big)$ ?

Sources

Browse retained paths and inspect the exact material available for this Problem.

3 retained statements2415f78e850a

Open selected source

FormalConjectures/ErdosProblems/

699.lean

Retained formal statement1 of 3

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

FormalConjectures/ErdosProblems/699.leanErdos699.erdos_6991 lineExact file

1True ↔ ∀ (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

Sources

Search problems.science