FormalConjectures.ErdosProblems.«396»

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import FormalConjecturesUtil

Erdős Problem 396

Reference: erdosproblems.com/396


namespace Erdos396


open Nat

Is it true that for every $k$ there exists $n$ such that $$\prod_{0\leq i\leq k}(n-i) \mid \binom{2n}{n}?$$

@[category research open, AMS 11]
theorem declaration uses 'sorry'erdos_396 : answer(sorry) ↔ ∀ k : ℕ, ∃ n : ℕ, descFactorial n (k + 1) ∣ centralBinom n := by⊢ True ↔ ∀ (k : ℕ), ∃ n, n.descFactorial (k + 1) ∣ n.centralBinom
  sorryAll goals completed! 🐙



-- TODO(firsching): formalise the additional material

end Erdos396