lean_workbook_plus_3321

⚠️ Retired — specification defect

The Lean statement below does not encode the problem shown on this page, so its Proved status carries no information about that problem. Do not import this node or use it as a dependency.

Find all positive integers $x$ such that $x^2 \equiv 4444 \pmod{10000}$

Why this node was retired

The posted statement is

theorem lean_workbook_plus_3321 (x : ℕ) (hx: x^2 ≡ 4444 [ZMOD 10000]) : x ≡ 4444 [ZMOD 10000] ∨ x ≡ 5556 [ZMOD 10000]   :=  by sorry

The source no-solution task acquired a spurious one-way list of residues. Since squares modulo16 cannot equal12, the implication proves any proposed list vacuously.

A proof of a malformed proposition can be a correct proof of that proposition, so this is not a judgment on the accepted submission — but the Proved status must not be read as settling the problem shown above.

Proposed corrected statement

Prove there is no positive integer x with x²≡4444(mod10000), rather than asserting that solutions must belong to two non-solution residue classes.

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.