lean_workbook_plus_16271

⚠️ 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.

For positive integers $a$ and $b$ , prove that $ab|a-b$ iff $a=b$ .

Why this node was retired

The posted statement is

theorem lean_workbook_plus_16271 : ∀ a b : ℕ, a * b ∣ a - b ↔ a = b   :=  by sorry

Positive inputs were not required and natural subtraction truncates a−b; even with positivity, a<b makes divisibility of0 automatic.

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 positive integers a,b use integer divisibility ab∣(a−b), or natural divisibility ab∣|a−b|, and prove iff a=b.

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.