FormalConjectures.ErdosProblems.«943»

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import FormalConjecturesUtil

Erdős Problem 943

Reference: erdosproblems.com/943


open AdditiveCombinatorics Nat Filter


namespace Erdos943

Let $A$ be the set of powerful numbers. Is is true that $1_A\ast 1_A(n)=n^{o(1)}$ for every $n$?

@[category research open, AMS 11]
theorem declaration uses 'sorry'erdos_943 : answer(sorry) ↔
    ∃ (o : ℕ → ℝ), o =o[atTop] (1 : ℕ → ℝ) ∧ ∀ᶠ n in atTop, (sumRep Powerful n) ≤ (n : ℝ)^(o n) := by⊢ True ↔ ∃ o, o =o[atTop] 1 ∧ ∀ᶠ (n : ℕ) in atTop, ↑(sumRep Powerful n) ≤ ↑n ^ o n
  sorryAll goals completed! 🐙


end Erdos943