A divisible sum gives a divisible sum of cubes

Proved

WorkbookSource.problem_57161

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

lean-workbooksource-checked

Given $a + b + c$ is divisible by 3, prove $a^3 + b^3 + c^3$ is also divisible by 3.

Source: InternLM Lean-Workbook, record lean_workbook_57161 (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_57161 (a b c : ℤ) (h : 3 ∣ a + b + c) : 3 ∣ a^3 + b^3 + c^3  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_57161; Apache-2.0

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