A sum of powers modulo2011

Proved

WorkbookSource.problem_16562

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

lean-workbooksource-checked

Apply Fermat's Little Theorem to each of the terms and prove that $(-5)^{2011}+3^{2011}+2^{2011}\equiv(-5+3+2)\pmod{2011}=0\pmod{2011}$ .

Source: InternLM Lean-Workbook, record lean_workbook_16562 (Apache-2.0). The complete source proposition and its explicit variable declarations are preserved.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.problem_16562 : (-5 : ℤ) ^ 2011 + 3 ^ 2011 + 2 ^ 2011 ≡ 0 [ZMOD 2011]  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_16562; Apache-2.0

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