lean_workbook_plus_58228

⚠️ 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.

Prove that $x^2\equiv1\pmod{p}$ has solutions $\pm1$ for all primes $p$

Why this node was retired

The posted statement is

theorem lean_workbook_plus_58228 (p : ℕ) (hp : Nat.Prime p) :
    ∃ x : ℕ, x^2 ≡ 1 [ZMOD p]   :=  by sorry

The source names both signs, while the formalization asks only for one witness. The supplied wording does not itself explicitly say these are the only solutions.

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

State both residue solutions+1 and−1; if a full classification is intended, state ∀x:ZMod p,x²=1↔x=1∨x=−1.

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.