Factoring an integer quartic

Proved

WorkbookSource.problem_4689

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

lean-workbooksource-checked

Express $n^4-20n^2+4$ as a product of two quadratic polynomials.

Source: InternLM Lean-Workbook, record lean_workbook_4689 (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_4689 : ∀ n : ℤ, n^4 - 20*n^2 + 4 = (n^2 - 4*n - 2)*(n^2 + 4*n - 2)  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_4689; Apache-2.0

View graph