lean_workbook_plus_390

Proved

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

Given is a sequence of positive integers, defined by $a_1=1$ and $a_{n+1}=a_n^2+a_n+1$ , for every positive integer $n$ . Prove that for every positive integer $n$ , $a_n^2+1 | a_{n+1}^2+1$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_390 (n : ℕ) (a : ℕ → ℕ) (a1 : a 0 = 1) (a_rec : ∀ n, a (n + 1) = a n ^ 2 + a n + 1) : (a n ^ 2 + 1) ∣ (a (n + 1) ^ 2 + 1)   :=  by sorry

Source

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

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