Odd powers preserve a zero sum

Proved

WorkbookSource.problem_20475

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

lean-workbooksource-checked

If $a + b = 0$ and $n$ is odd, prove that $a^n + b^n = 0$

Source: InternLM Lean-Workbook, record lean_workbook_20475 (Apache-2.0). The complete source proposition and explicit variable declarations are preserved.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.problem_20475 (a b : ℝ) (n : ℕ) (hn : Odd n) (hab : a + b = 0) : a^n + b^n = 0  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_20475; Apache-2.0

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