lean_workbook_plus_61418

Proved

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

Let $a$ and $b$ be positive integers with $a>1$ and $b>2$ . Prove that $a^b+1\ge b(a+1)$ and determine when there is inequality.

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_61418 (a b : ℕ) (ha : a > 1) (hb : b > 2) : a^b + 1 ≥ b * (a + 1)   :=  by sorry

Source