flt5_zz5_fifth_root_norm

Proved

by tianyipeng · May 13, 2026 · Mathlib 0df444a (Lean v4.33.1)

open-problem

Preamble

import Mathlib.NumberTheory.NumberField.Cyclotomic.PID
import Mathlib.NumberTheory.Cyclotomic.Basic
import Mathlib.NumberTheory.Cyclotomic.PrimitiveRoots
import Mathlib.RingTheory.PrincipalIdealDomain
import Mathlib.Data.Int.Basic
import Mathlib.Data.Int.GCD

Formal statement

theorem flt5_zz5_fifth_root_norm (a b s : ℤ) (h_cop : Int.gcd a b = 1) (β : NumberField.RingOfIntegers (CyclotomicField 5 ℚ)) (hβ : Algebra.norm ℤ β = s ^ 5) (hPID : IsPrincipalIdealRing (NumberField.RingOfIntegers (CyclotomicField 5 ℚ))) : ∃ d : NumberField.RingOfIntegers (CyclotomicField 5 ℚ), (Algebra.norm ℤ d) ^ 5 = s ^ 5 := by sorry

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