938.lean`

Explanation legend Lean4 Domain Explanation Language (L4DEL)

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L4DEL: Lean4 Domain Explanation Language

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Credit: The upstream authors and contributors retain credit for the project and mathematics. lean4-explainer only renders their pinned source and adds the separately disclosed explanation layer.

Project sources: Pinned project documentation, Formal Conjectures paper, arXiv v1

1 declarations, 1 contain sorry, 0 declared as axioms

Erdős Problem 938

Reference: erdosproblems.com/938

Imports (1)

FormalConjecturesUtil

theorem Erdos938.erdos_938 Let $A=\{n_1 < n_2 < \cdots\}$ be the sequence of powerful numbers (if $p\mid n$ then $p^2\mid n$) sorry line 37 source
Source documentation
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 $n_k,n_{k+1},n_{k+2}$?

depends on sorry what this means
Statement uses: Iff, True, Set.Finite, Finset, Nat, Set.ofPred, And, Set.IsAPOfLength, OfNat.ofNat, ENat, Exists, Eq, Insert.insert, Nat.nth, Nat.Powerful, HAdd.hAdd, Singleton.singleton
Proof uses: sorryAx, Lean.Name, Bool.false, Lean.Name.num, Lean.Name.str, Lean.Name.anonymous
26 instances, coercions and auxiliary constants left out.

Tactic trace: 1 steps
Open to load the checked before-and-after goal states.
```
theorem 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
…
```