Skip to content

Erdős problem 698

Is there some h(n)→∞h(n)\to \infty such that for all 2≤i<j≤n/22\leq i<j\leq n/2 gcd((ni),(nj))≥h(n)?\textrm{gcd}\left( \binom{n}{i},\binom{n}{j}\right) \geq h(n)?

No current result

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

Retained declaration

FormalConjectures/ErdosProblems/698.lean

Formal Conjectures

FormalConjectures/ErdosProblems/698.leanErdos698.erdos_6984 linesExact file
True ↔  ∃ h,    Filter.Tendsto h Filter.atTop Filter.atTop ∧      ∀ (n i j : ℕ), 2 ≤ i → i < j → j ≤ n / 2 → h n ≤ (n.choose i).gcd (n.choose j)
SolvedStatement only, no proof

Proof manifests naming this Problem

  • Jayyhk Erdős Leanjayyhk:erdos:698
  • PLBY Lean proofsErdosProblems.Erdos698

Reported activity

Work these sources record against this Problem. Source-reported attribution, not reviewed here.

Continue

Start a contributionBrowse the source filesOpen the collection entry

Search problems.science

Find a Problem, Result, source, or page