lean_workbook_plus_26997

⚠️ 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.

Rewrite the equation as $a^2 + b^2 + c^3 = 100a + 10b + c \iff c^3 - c = 100a - a^2 + 10b - b^2$ . Now examine the values of $c^3 - c, 100a - a^2$ , and $10b - b^2$ as each variable ranges from 1 to 9.

Why this node was retired

The posted statement is

theorem lean_workbook_plus_26997 :
  ∀ a b c : ℕ,
    1 ≤ a ∧ a ≤ 9 ∧
    1 ≤ b ∧ b ≤ 9 ∧
    1 ≤ c ∧ c ≤ 9 →
    a^2 + b^2 + c^3 = 100 * a + 10 * b + c ↔ c^3 - c = 100 * a - a^2 + 10 * b - b^2   :=  by sorry

The range restriction is scoped inside only the left side of an iff; outside-range inputs can make that implication vacuous.

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

Proposed corrected statement

For1≤a,b,c≤9 parenthesize the conclusion as the equivalence of the two equations. Check the natural subtractions are exact under these digit bounds.

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.