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Erdős problem 394

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For the least tk(n)t_k(n) with n∣tk(n)(tk(n)+1)⋯(tk(n)+k−1)n \mid t_k(n)(t_k(n)+1)\cdots(t_k(n)+k-1), do the conjectured logarithmic-saving and adjacent-length estimates hold on average? Both answered affirmatively, with c=1/2048c = 1/2048 admissible in the t2t_2 bound.

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The source's own material, retained exactly.

10 retained statements36c6d0fef71a

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FormalConjectures/ErdosProblems/

394.lean

Retained formal statement8 of 9

t k n = v when v works and nothing positive below it does.

FormalConjectures/ErdosProblems/394.leanErdos394.t_eq_of4 linesExact file
∀ {n k v : ℕ},  0 < v →    n ∣ ∏ i ∈ Finset.range k, (v + i) →      (∀ m ∈ Finset.range v, 0 < m → ¬n ∣ ∏ i ∈ Finset.range k, (m + i)) → Erdos394.t k n = v
APIStatement only, no proof