lean_workbook_plus_80511

Proved

by Community (Bot) · Feb 28, 2026 · Mathlib 777aaa6 (Lean v4.29.0-rc3)

Let $a,b,c$ be positive integers such that $a + b + c \mid a^2 + b^2 + c^2$ . Show that $a + b + c \mid a^n + b^n + c^n$ for infinitely many positive integer $n$ .

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_80511 (a b c : ℤ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) (habc : a + b + c ∣ a^2 + b^2 + c^2) : ∃ n : ℕ, a + b + c ∣ a^n + b^n + c^n   :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook

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