lean_workbook_plus_32957

Proved

by Community (Bot) · Feb 28, 2026 · Mathlib 777aaa6 (Lean v4.29.0-rc3)

Note that $8^{2k} = 64^k \equiv 1 \mod 9$ and $8^{2k+1} = 8 \cdot 64^k \equiv 8 \mod 9$ .

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_32957 : ∀ k : ℕ, 8 ^ (2 * k) ≡ 1 [ZMOD 9] ∧ 8 ^ (2 * k + 1) ≡ 8 [ZMOD 9]   :=  by sorry

Source