Erdős problem 394

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.

Sources

The source's own material, retained exactly.

10 retained statements36c6d0fef71a

FormalConjectures/ErdosProblems/

394.lean

Retained formal statement3 of 9

They proved (with Selfridge) that this holds for $n=10$ .

FormalConjectures/ErdosProblems/394.leanErdos394.erdos_394.variants.factorial_gap_101 lineExact file

1∀ (k : ℕ), 2 ≤ k → k < 10 → Erdos394.t k (Nat.factorial 10) < Erdos394.t (k - 1) (Nat.factorial 10) - 1

SolvedStatement only, no proof