lean_workbook_plus_48545

Proved

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

Let $a, b, c$ be integers satisfying $ab + bc + ca = 1.$ Prove that $(1+ a^2 )(1+ b^2 )(1+ c^2 )$ is a perfect square.

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_48545 (a b c : ℤ) (hab : a * b + b * c + c * a = 1) : ∃ k : ℤ, k ^ 2 = (1 + a ^ 2) * (1 + b ^ 2) * (1 + c ^ 2)   :=  by sorry

Source

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

View graph