lean_workbook_plus_33225

Proved

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

Find the necessary and sufficient condition for numbers $a\in\mathbb Z\setminus \{-1,0,1\}$ , $b,c\in\mathbb Z\setminus \{0\}$ , and $d\in\mathbb N\setminus\{0,1\}$ for which $a^n+bn+c$ is divisible by $d$ for each natural number $n.$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_33225 (a b c d : ℤ) (n : ℕ) : (a^n + b*n + c) % d = 0 ↔ (d ∣ a^n + b*n + c)   :=  by sorry

Source

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

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