Is it true that for every $n \geq 1$ there is a $k$ such that $n (n + 1) \dots (n + k - 1) ∣ (n + k) \dots (n + 2 k - 1)?$

Worked, still open.

number theory · open · formalized (Lean) · 0 attempts

use this record

vela registry pull vfr_37aec80d874a0239

vela reproduce examples/erdos-problems

evidence

unverified AI candidates (2)

gpt-erdos · GPT-5.2 Pro + Deep Research · unverified

✅ **Empirically (and very plausibly in general): yes, it appears to be true**, i.e.

llm-hunter · gpt pro 5.2 · unverified

1 LLM attack(s) recorded (gpt pro 5.2); unverified.

AMS 11 · open (literature)

theorem erdos_389 : answer(sorry) ↔
    ∀ n ≥ 1, ∃ k ≥ 1, ∏ i ∈ Finset.range k, (n + i) ∣ ∏ i ∈ Finset.range k, (n + k + i)

open