lean_workbook_plus_80221

⚠️ 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 $2$ is a quadratic residue modulo $p$ , where $p$ is a prime, if and only if $p$ is congruent to 1 or -1 modulo $8$ .

Why this node was retired

The posted statement is

theorem lean_workbook_plus_80221 : ∀ p : ℕ, p.Prime → (2 : ZMod p) ^ 2 = 1 ↔ p ≡ 1 [ZMOD 8] ∨ p ≡ -1 [ZMOD 8]   :=  by sorry

The target uses2²=1 instead of existence of a square root of2, and the usual criterion excludes p=2.

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 an odd prime p, state IsSquare(2:ZMod p) iff p≡1 or−1 modulo8.

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.