A sum of powers modulo thirteen

Proved

WorkbookSource.problem_30022

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

lean-workbooksource-checked

With $\mod13, 333^{555}+555^{777}+777^{333} \equiv5+1-1\equiv5\mod13$

Source: InternLM Lean-Workbook, record lean_workbook_30022 (Apache-2.0). The complete source proposition and explicit variable declarations are preserved.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.problem_30022 :
  (333^555 + 555^777 + 777^333) % 13 = 5  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_30022; Apache-2.0

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