A power of two modulo thirteen

Proved

WorkbookSource.problem_18636

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

lean-workbooksource-checked

Find the remainder when $2^{2009}$ is divided by $13$ .

Source: InternLM Lean-Workbook, record lean_workbook_18636 (Apache-2.0). The complete source proposition and explicit variable declarations are preserved.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.problem_18636 : 2 ^ 2009 ≡ 6 [ZMOD 13]  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_18636; Apache-2.0

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