∀ {K : Type u_1} [inst : Field K] {ζ : K} {hζ : IsPrimitiveRoot ζ 3} (S : FermatLastTheoremForThreeGen.Solution hζ)
  [inst_1 : NumberField K] [IsCyclotomicExtension {3} ℚ K] {p : NumberField.RingOfIntegers K},
  Prime p → p ∣ S.a + ↑⋯.unit * S.b → p ∣ S.a + ↑⋯.unit ^ 2 * S.b → Associated p (hζ.toInteger - 1)