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Erdős problem 683

There exists c>0c > 0 such that P(n,k)>min⁡{n−k+1,k1+c}P(n, k) > \min\{n-k+1, k^{1 + c}\} for all 0<k<n0 < k < n.}

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The source's own material, retained exactly.

4 retained statements36c6d0fef71a

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FormalConjectures/ErdosProblems/

683.lean

Retained formal statement4 of 4

Sylvester and Schur [Er34] proved that P(n,k)>kP(n, k) > k for k≤n/2k \le n/2.

FormalConjectures/ErdosProblems/683.leanErdos683.erdos_683.variant.sylvester_schur1 lineExact file
∀ (n k : ℕ), 0 < k ∧ k ≤ n / 2 → Erdos683.P n k > k
SolvedStatement only, no proof