lean_workbook_plus_23725

Proved

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

Proove that, for any $n$ non-negative integer, the number $1^n + 2^n + 3^n + 4^n$ is divisible by 5 if, and only if, $n$ is not divisible by 4.

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_23725 (n:ℕ) : n % 4 ≠ 0 ↔ (1^n + 2^n + 3^n + 4^n) % 5 = 0   :=  by sorry

Source