lean_workbook_plus_37009

⚠️ 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.

$\Rightarrow \, (2005-i)^{2005}\equiv-i^{2005}(mod \quad 2005)$

Why this node was retired

The posted statement is

theorem lean_workbook_plus_37009 (i : ℤ) (hi : i * i = -1) : (2005 - i) ^ 2005 ≡ (-i) ^ 2005 [ZMOD 2005]   :=  by sorry

The accepted proof only contradicts the impossible integer square; the underlying power congruence itself needs no such premise.

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

Remove the impossible integer premise i²=−1 for the valid integer congruence. If i denotes the imaginary unit in the full source, instead work in the Gaussian integers modulo the ideal(2005).

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.