Three exact power congruences modulo seven

Proved

WorkbookSource.problem_15540

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

lean-workbooksource-checked

$2^3\equiv 1(7)\Rightarrow 2^{348}\equiv 1(7)\Rightarrow 2^{349}\equiv 2(7)$

Source: InternLM Lean-Workbook, record lean_workbook_15540 (Apache-2.0). The complete source proposition and explicit variable declarations are preserved.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.problem_15540 : (2^3 ≡ 1 [MOD 7]) ∧ (2^348 ≡ 1 [MOD 7]) ∧ (2^349 ≡ 2 [MOD 7])  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_15540; Apache-2.0

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