FormalConjectures.ErdosProblems.«371»

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import FormalConjecturesUtil

Erdős Problem 371

Reference: erdosproblems.com/371


namespace Erdos371

Let $P(n)$ denote the largest prime factor of $n$. Show that the set of $n$ with $P(n+1) > P(n)$ has density $\frac{1}{2}$.

@[category research open, AMS 11]
theorem declaration uses 'sorry'erdos_371 :
    { n | Nat.maxPrimeFac (n + 1) > Nat.maxPrimeFac n }.HasDensity (1/2) := by⊢ {n | (n + 1).maxPrimeFac > n.maxPrimeFac}.HasDensity (1 / 2)
  sorryAll goals completed! 🐙


-- TODO: add the statements from the additional material
end Erdos371