erdős #826
Are there infinitely many such that, for all ,
Worked, still open.
number theory · open · formalized (Lean) · 0 attempts
use this record
vela registry pull vfr_37aec80d874a0239vela reproduce examples/erdos-problemsevidence
unverified AI candidates (2)
gpt-erdos · GPT-5.2 Pro + Deep Research · unverified
Interpreting “(\ll)” in the usual analytic-number-theory way [[nomath]](an **absolute** implied constant, independent of both $n$ and $k$)[[/nomath]], this is **open**.
candidate solution ↗llm-hunter · gpt pro 5.2 · unverified
1 LLM attack(s) recorded (gpt pro 5.2); unverified.
candidate solution ↗formal
AMS 11 · open (literature)
theorem erdos_826 : answer(sorry) ↔
∃ C > (0 : ℝ), { n | ∀ k ≥ 1, σ 0 (n + k) ≤ C * k }.Infiniteformal-conjectures/826.lean ↗status
open