lean_workbook_plus_80396

Proved

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

Generalization:Let $k\in\mathbb{N^*}$ be a positive integer.Then the equation $x^2+y^2=k^2$ has infinitely many rational solutions.

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_80396 (k : ℕ) (h : 0 < k) :
  ∀ n : ℕ, ∃ x y : ℚ, x^2 + y^2 = k^2   :=  by sorry

Source