A coefficient sum from a polynomial value at one

Proved

WorkbookSource.problem_13032

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

lean-workbooksource-checked

Find $a+b+c+d$ given the function $f(x)=ax^3+bx^2+cx+d$ and the following conditions: $f(0)=4$ , $f(1)=10$ , $f(2)=26$ , $f(-1)=2$ .

Source: InternLM Lean-Workbook, record lean_workbook_13032 (Apache-2.0). The complete source proposition and explicit variable declarations are preserved.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.problem_13032 (a b c d : ℝ) (h₁ : a*0^3 + b*0^2 + c*0 + d = 4) (h₂ : a*1^3 + b*1^2 + c*1 + d = 10) (h₃ : a*2^3 + b*2^2 + c*2 + d = 26) (h₄ : a*(-1)^3 + b*(-1)^2 + c*(-1) + d = 2) : a + b + c + d = 10  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_13032; Apache-2.0

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