lean_workbook_plus_79564

Proved

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

$521$ is a prime number. Then $8^{520} = 1\pmod{521}$ and so $8^{520\times 521} = 1\pmod{521}$ and so $8^{m + 520\times 521} + 9(m + 520\times 521)^2$ $= 8^m + 9m^2\pmod {521}$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_79564  (m : ℕ)
  (h₀ : 0 < m)
  (h₁ : Nat.Prime 521)
  (h₂ : 8^520 % 521 = 1) :
  (8^(m + 520 * 521) + 9 * (m + 520 * 521)^2) % 521 = (8^m + 9 * m^2) % 521   :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook

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