lean_workbook_plus_27973

⚠️ 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.

Prove that the sequence $a_n = 3^n- 2^n$ contains no three numbers in geometric progression.

Why this node was retired

The posted statement is

theorem lean_workbook_plus_27973 (a : ℕ → ℕ) (a_n_def : ∀ n, a n = 3^n - 2^n) : ¬ (∃ k : ℕ, ∃ m : ℕ, ∃ n : ℕ, a k = a m * a n)   :=  by sorry

A geometric progression was encoded as a_k=a_m a_n rather than a_m²=a_k a_n, and repeated/zero indices were not excluded.

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

Proposed corrected statement

For the positive sequence a_n=3^n−2^n (n≥1), formulate the intended nonexistence as no distinct ordered indices k<m<n with a_m²=a_k a_n, then prove or investigate that exact claim.

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.