lean_workbook_plus_71690

⚠️ 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.

Prove that if $a,b,c$ are positive integers such that $abcd=a^2+b^2+c^2+1$ and $d \neq 4$, then $cd = 4$ implies $d = 4$.

Why this node was retired

The posted statement is

theorem lean_workbook_plus_71690 (a b c d : ℤ) (h1 : a * b * c * d = a ^ 2 + b ^ 2 + c ^ 2 + 1) (h2 : d ≠ 4) (h3 : c * d = 4) : d = 4   :=  by sorry

The positive-variable restrictions were dropped, admitting c=−1,d=−4.

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

Proposed corrected statement

Require a,b,c>0 as integers (and infer d>0 from the equation or state it); keep cd=4 and prove d=4, or equivalently show the assumptions together with d≠4 are inconsistent.

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.