lean_workbook_plus_20769

⚠️ 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.

Find all the triplets of real numbers $(x , y , z)$ such that : $y=\frac{x^3+12x}{3x^2+4}$ , $z=\frac{y^3+12y}{3y^2+4}$ , $x=\frac{z^3+12z}{3z^2+4}$

Why this node was retired

The posted statement is

theorem lean_workbook_plus_20769 : ∀ x y z : ℝ, (y = x^3 + 12*x / (3*x^2 + 4) ∧ z = y^3 + 12*y / (3*y^2 + 4) ∧ x = z^3 + 12*z / (3*z^2 + 4)) ↔ x = -2 ∨ x = 0 ∨ x = 2   :=  by sorry

Whole numerators lost parentheses, and the conclusion ignores y,z.

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

Proposed corrected statement

Restore the three source rational maps and classify all triples, including y,z and the fixed-point restrictions, rather than only listing possible x.

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.