Are there infinitely many $n$ such that, for all $k \geq 1$ , $ω (n + k) ≪ k ?$ (Here $ω (n)$ is the number of distinct prime divisors of $n$ .)

Worked, still open.

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

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vela registry pull vfr_37aec80d874a0239

vela reproduce examples/erdos-problems

formal

AMS 11 · solved (literature)

theorem erdos_248 : (∃ C > (0 : ℝ), { n | ∀ k ≥ 1, ω (n + k) ≤ C * k }.Infinite)

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