Theorems · Theorem · complex analysis
Complex.isPrimitiveRoot_iff
∀ (ζ : ℂ) (n : ℕ), n ≠ 0 → (IsPrimitiveRoot ζ n ↔ ∃ i < n, ∃ (_ : i.Coprime n), Complex.exp (2 * ↑Real.pi * Complex.I * (↑i / ↑n)) = ζ)
- Defined in
- Mathlib.RingTheory.RootsOfUnity.Complex
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 198 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Complexstatement and proof · cited by 5,565
- Nat.cast_zeroproof · cited by 1,870
- Real.pistatement and proof · cited by 1,774
- Complex.ofRealstatement and proof · cited by 1,654
- Complex.Istatement and proof · cited by 866
- Complex.expstatement and proof · cited by 612
- IsPrimitiveRootstatement and proof · cited by 356
- IsPrimitiveRoot.pow_eq_oneproof · cited by 48
- IsPrimitiveRoot.eq_pow_of_pow_eq_oneproof · cited by 17
- Complex.isPrimitiveRoot_expproof · cited by 14
- Complex.exp_nat_mulproof · cited by 8
- IsPrimitiveRoot.pow_iff_coprimeproof · cited by 3
Cited by1
Results whose statement or proof uses this declaration.
- IsPrimitiveRoot.argproof · cited by 0