lean_workbook_plus_24342

Disproved

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

The equation $x^4+py^4=z^4$ has no solution $(x,y,z) \in\mathbb N^3$ with the given prime number $p,p\equiv 3(mod4)$ or something else?

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_24342 (p : ℕ) (hp : p.Prime) (hp_mod_4_eq_3 : p ≡ 3 [ZMOD 4]) : ¬∃ (x y z : ℕ), (x ^ 4 + p * y ^ 4 = z ^ 4)   :=  by sorry

Source