GCD_and_LCM_from_Prime_Decomposition

⚠️ 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.

gcd(m,n) has prime factorization with exponents being the min of corresponding exponents of m and n.

Why this node was retired

The posted statement is

theorem GCD_and_LCM_from_Prime_Decomposition (m n : ℕ) (p : ℕ) (hp : Nat.Prime p) : (Nat.gcd m n).factorization p = min (m.factorization p) (n.factorization p) := by sorry

Zero inputs are included although finite factorization represents zero by the zero function.

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 m≠0 and n≠0.

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.