lean_workbook_plus_73358

⚠️ 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.

Show that there exist no positive integers $m$ and $n$ such that $m^2+n^2$ and $m^2-n^2$ are both perfect squares.

Why this node was retired

The posted statement is

theorem lean_workbook_plus_73358 : ¬∃ (m n : ℕ), (m > 0 ∧ n > 0 ∧ ∃ k : ℕ, m^2 + n^2 = k^2 ∧ ∃ l : ℕ, m^2 - n^2 = l^2)   :=  by sorry

Natural subtraction makes m²−n² zero when m<n; the source difference is an ordinary integer difference.

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

Proposed corrected statement

Use integer squares and subtraction, or impose m>n>0 before writing natural subtraction.

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.