Self-inverse nonzero residues modulo a prime

Proved

WorkbookRestored.plus_42229

by wamlart · Sep 12, 2026 · Mathlib 777aaa6 (Lean v4.29.0-rc3)

lean-workbookrestored-importssource-checked

For a prime $p$ and nonzero residue $a\in\mathbb Z/p\mathbb Z$ , $a=a^{-1}$ if and only if $a=1$ or $a=p-1$ .

This restores the missing imports or namespaces of the original node, retaining its formal proposition. Source: Lean-Workbook row lean_workbook_plus_42229 (Apache-2.0).

Preamble

import Mathlib.Analysis.Complex.Basic
import Mathlib.Data.ZMod.Basic
open Nat

Formal statement

theorem WorkbookRestored.plus_42229 (p : ℕ) (hp : p.Prime) (a : ZMod p) (ha : a ≠ 0) : a = a⁻¹ ↔ a = 1 ∨ a = p-1   :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, row lean_workbook_plus_42229; original Prove2Me node e2eab018-45bd-45c6-9c75-6e8909248e28; Apache-2.0

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