A determinant formed from pairwise sums of powers

Proved

WorkbookRestored.plus_15411

by wamlart · Sep 12, 2026 · Mathlib 777aaa6 (Lean v4.29.0-rc3)

lean-workbookrestored-importssource-checked

For real $a,b,c$ ,

\det\begin{pmatrix}a+b&b+c&c+a\\a^2+b^2&b^2+c^2&c^2+a^2\\a^3+b^3&b^3+c^3&c^3+a^3\end{pmatrix}=2abc(a-b)(b-c)(c-a).

This restores the missing imports or namespaces of the original node, retaining its formal proposition. Source: Lean-Workbook row lean_workbook_plus_15411 (Apache-2.0).

Preamble

import Mathlib.Analysis.Complex.Basic
import Mathlib.LinearAlgebra.Matrix.Determinant.Basic
open Matrix

Formal statement

theorem WorkbookRestored.plus_15411 (a b c : ℝ) : Matrix.det (![![a+b, b+c, c+a],![a^2+b^2, b^2+c^2, c^2+a^2],![a^3+b^3, b^3+c^3, c^3+a^3]]) = 2*a*b*c*(a-b)*(b-c)*(c-a)   :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, row lean_workbook_plus_15411; original Prove2Me node 38957f25-5b28-4e75-be65-d7459034c281; Apache-2.0

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