lean_workbook_plus_44656

⚠️ 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.

For $r=2$ and $n=14$, find the number of quadratic residues.

Why this node was retired

The posted statement is

theorem lean_workbook_plus_44656  (S : Finset ℕ)
  (h₀ : ∀ (a : ℕ), a ∈ S ↔ a < 14 ∧ a ≠ 0 ∧ a^2 % 14 = 1) :
  S.card = 4   :=  by sorry

The formal statement changes or incorrectly supplies part of the source problem; the accepted note identifies a concrete witness or definitional mechanism.

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

Proposed corrected statement

Distinguish square residues from roots of one. To count quadratic residues modulo 14, define {r∈{0,…,13}:∃a,r≡a² mod 14}, explicitly choosing whether zero and nonunits count; then determine its cardinality. For the stored roots-of-one condition the correct cardinality is 2.

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.