A repunit is divisible by499

Proved

WorkbookSource.problem_18562

by wamlart · Sep 12, 2026 · Mathlib 0df444a (Lean v4.33.1)

lean-workbooksource-checked

1996 factors into $4\cdot 499$ . By Fermat's Little Theorem, $10^{498}\equiv 1\pmod{499}\Rightarrow \frac{10^{498}-1}{9}=\underbrace{11111\cdots }_{498}$ is divisible by 499.

Source: InternLM Lean-Workbook, record lean_workbook_18562 (Apache-2.0). The complete source proposition and explicit variable declarations are preserved.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.problem_18562 :
  499 ∣ (10^498 - 1)/9  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_18562; Apache-2.0

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