Erdős problem 394 · problems.science

For the least $t_k(n)$ with $n \mid t_k(n)(t_k(n)+1)\cdots(t_k(n)+k-1)$ , do the conjectured logarithmic-saving and adjacent-length estimates hold on average? Both answered affirmatively, with $c = 1/2048$ admissible in the $t_2$ bound.

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10 retained statements2415f78e850a

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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

1∀ {n k v : ℕ},2  0 < v →3    n ∣ ∏ i ∈ Finset.range k, (v + i) →4      (∀ m ∈ Finset.range v, 0 < m → ¬n ∣ ∏ i ∈ Finset.range k, (m + i)) → Erdos394.t k n = v

APIStatement only, no proof

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