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Erdős problem 729

Let C>0C>0 be a constant. Are there infinitely many integers a,b,na,b,n with a+b>n+Clog⁡na+b> n+C\log n such that the denominator of n!a!b!\frac{n!}{a!b!}contains only primes ≪C1\ll_C 1?

No current result

No reviewed Result is current in Vela Mathematics Program. Retained source material is shown below.

Retained declaration

FormalConjectures/ErdosProblems/729.lean

Formal Conjectures

FormalConjectures/ErdosProblems/729.leanErdos729.erdos_72910 linesExact file
True ↔  ∀ C > 0,    ∃ K ≥ 3,      {(a, b, n) |          a > 0 ∧            b > 0 ∧              n > 0 ∧                ↑a + ↑b > ↑n + C * Real.log ↑n ∧                  ∀ (p : ℕ),                    Nat.Prime p → p > K → padicValNat p (↑n.factorial / (↑a.factorial * ↑b.factorial)).den = 0}.Infinite
SolvedProof has a holelean4external proof

The proof uses `sorry`: part of the argument is written but not proved. Lean accepts the file; it does not accept the theorem.

Proof manifests naming this Problem

  • Jayyhk Erdős Leanjayyhk:erdos:729
  • PLBY Lean proofsErdosProblems.Erdos729

Reported activity

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