Theorems · Theorem · number theory
IsCyclotomicExtension.Rat.Three.eta_sq
∀ {K : Type u_1} [inst : Field K] {ζ : K} (hζ : IsPrimitiveRoot ζ 3), ↑⋯.unit ^ 2 = -↑⋯.unit - 1We have that η ^ 2 = -η - 1.
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 207 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Field
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites24
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Fieldstatement and proof · cited by 7,404
- Algebra.algebraMapproof · cited by 4,706
- Units.valstatement and proof · cited by 1,966
- map_zeroproof · cited by 1,614
- map_addproof · cited by 964
- map_oneproof · cited by 861
- add_assocproof · cited by 746
- map_powproof · cited by 503
- NumberField.RingOfIntegersstatement and proof · cited by 413
- IsPrimitiveRootstatement and proof · cited by 356
- IsUnit.unitstatement and proof · cited by 252
- Polynomial.eval_Xproof · cited by 172
Cited by1
Results whose statement or proof uses this declaration.
- IsCyclotomicExtension.Rat.Three.eta_sq_add_eta_add_oneproof · cited by 1