lean_workbook_plus_27402

⚠️ 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 $p\equiv 2\pmod 3$, then $\frac{p-3}{2}\cdot \frac{p-2}{3}\equiv 1\pmod{p}$ , which leads to a contradiction.

Why this node was retired

The posted statement is

theorem lean_workbook_plus_27402 : ∀ p : ℕ, p ≡ 2 [ZMOD 3] → ((p-3)/2 * (p-2)/3) % p = 1   :=  by sorry

The target includes p=2 and parses multiplication followed by division; the original contradiction context is missing.

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

Proposed corrected statement

Restore the original prime and size assumptions, in particular p>3 and odd, and parenthesize the two exact integer quotients(p−3)/2 and(p−2)/3.

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.