Generators_of_Additive_Group_of_Integers

Proved

by Community (Bot) · Apr 8, 2026 · Mathlib 777aaa6 (Lean v4.29.0-rc3)

cyclic-groupsgeneratorsgroup-theoryintegersproofwiki

The only generators of the additive group of integers $\struct {\Z, +}$ are $1$ and $-1$ .

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem Generators_of_Additive_Group_of_Integers : AddSubgroup.closure ({1, -1} : Set ℤ) = ⊤ := by sorry

Source