lean_workbook_plus_30586

⚠️ Retired — specification defect

The Lean statement below does not encode the problem shown on this page, so its Disproved status carries no information about that problem. Do not import this node or use it as a dependency.

An integer sequence satisfies $a_{n+1}={a_n}^3 +1999$. Show that it contains at most one square.

Why this node was retired

The posted statement is

theorem lean_workbook_plus_30586 (a : ℕ → ℤ) (h : ∀ n, a (n + 1) = a n ^ 3 + 1999) : ∃ k, ∀ n, n ≠ k ∧ a n = a k ^ 2   :=  by sorry

The formal statement changes or incorrectly supplies part of the source problem; the accepted note identifies a concrete witness or definitional mechanism.

The recorded counterexample refutes the statement as encoded. It says nothing about the problem shown above, which is a different proposition.

Proposed corrected statement

State that {n∈ℕ:∃z∈ℤ,a_n=z²} has cardinality at most one, or equivalently any two square-valued indices are equal. The posted ∃k∀n,n≠k∧a_n=a_k² is unrelated and self-contradictory.

Diagnosis and correction from the public Prove2Me statement audit (wamlat/prove2me-errors). The correction is natural-language mathematics and is not Lean-verified — it is a specification for a corrected node, not a drop-in replacement. No corrected replacement node exists yet.