lean_workbook_plus_10999

Proved

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

If a,b,c are positive integers and $a+b+c=1$ prove that $5(a^{2}+b^{2}+c^{2})\leq 6(a^{3}+b^{3}+c^{3})+1$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_10999 (a b c : ℕ) (hab : a + b + c = 1) : 5 * (a ^ 2 + b ^ 2 + c ^ 2) ≤ 6 * (a ^ 3 + b ^ 3 + c ^ 3) + 1   :=  by sorry

Source