lean_workbook_plus_3642

⚠️ Retired — specification defect

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

Find all $f :\mathbb{Z}\rightarrow \mathbb{R_+}$ , $f(k)+\frac{4}{[f(k+1)]^2}=3$ for all $k> 0$ .

Why this node was retired

The posted statement is

theorem lean_workbook_plus_3642 (f : ℤ → ℝ) (hf: ∀ k > 0, f k + 4 / (f (k + 1))^2 = 3) : ∃ k, 0 < k ∧ ∀ k > 0, f k + 4 / (f (k + 1))^2 = 3   :=  by sorry

The classification question is replaced by an unused positive witness and the original hypothesis.

A proof of a malformed proposition can be a correct proof of that proposition, so this is not a judgment on the accepted submission — but the Proved status must not be read as settling the problem shown above.

Proposed corrected statement

Restore f:ℤ→ℝ with positivity and ask for a complete iff-classification of the functions satisfying the equation for positive k; an existential dummy index is not a classification. The solution family must be established independently.

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.