FormalConjectures.ErdosProblems.«938»

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import FormalConjecturesUtil

Erdős Problem 938

Reference: erdosproblems.com/938

open Nat


namespace Erdos938

Let $A={n_1 < n_2 < \cdots}$ be the sequence of powerful numbers (if $p\mid n$ then $p^2\mid n$). Are there only finitely many three-term progressions of consecutive terms $n_k,n_{k+1},n_{k+2}$?

@[category research open, AMS 11]
theorem declaration uses 'sorry'erdos_938 : answer(sorry) ↔ {P : Finset ℕ | (P : Set ℕ).IsAPOfLength 3 ∧ ∃ k,
    P = {nth Powerful k, nth Powerful (k + 1), nth Powerful (k + 2)}}.Finite := by⊢ True ↔ {P | (↑P).IsAPOfLength 3 ∧ ∃ k, P = {nth Powerful k, nth Powerful (k + 1), nth Powerful (k + 2)}}.Finite
  sorryAll goals completed! 🐙


end Erdos938