lean_workbook_plus_58694

⚠️ 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 for some integer $n$ the number $n^2 +1$ cant have factor of a form $4k+3$

Why this node was retired

The posted statement is

theorem lean_workbook_plus_58694 : ∃ n : ℤ, ¬ ∃ k : ℤ, n^2 + 1 ≡ 0 [ZMOD 4 * k + 3]   :=  by sorry

Ordinary positive-factor language was formalized using unrestricted integer k, admitting the divisor−1.

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 positive divisors d=4k+3, for example k:ℕ, and state that no such d divides n²+1 for any integer n.

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.