Are there infinitely many $n$ such that the largest prime factor of $n$ is $< n^{1/2}$ and the largest prime factor of $n + 1$ is $< (n + 1)^{1/2}$ ?

Worked, still open.

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

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formal

AMS 11 · solved (literature)

theorem erdos_370 : answer(True) ↔
    { n | Nat.maxPrimeFac n < √n ∧ Nat.maxPrimeFac (n + 1) < √(n + 1) }.Infinite

solved