Polynomial value differences are divisible by input differences

Proved

WorkbookRestored.plus_29341

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

lean-workbookrestored-importssource-checked

For an integer polynomial $P$ and distinct integers $a,b$ , $a-b$ divides $P(a)-P(b)$ .

This restores the missing imports or namespaces of the original node, retaining its formal proposition. Source: Lean-Workbook row lean_workbook_plus_29341 (Apache-2.0).

Preamble

import Mathlib.Analysis.Complex.Basic
import Mathlib.Algebra.Polynomial.Derivative
import Mathlib.Algebra.Polynomial.Eval.Defs
import Mathlib.Algebra.Polynomial.Roots
open Polynomial

Formal statement

theorem WorkbookRestored.plus_29341 (P : Polynomial ℤ) {a b : ℤ} (h : a ≠ b) : a - b ∣ P.eval a - P.eval b   :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, row lean_workbook_plus_29341; original Prove2Me node 576b1508-4e49-420b-bbc9-fa06cec2b04d; Apache-2.0

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