Theorems · Theorem · complex analysis
IsPrimitiveRoot.arg_eq_pi_iff
∀ {n : ℕ} {ζ : ℂ}, IsPrimitiveRoot ζ n → n ≠ 0 → (ζ.arg = Real.pi ↔ ζ = -1)- Defined in
- Mathlib.RingTheory.RootsOfUnity.Complex
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 196 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement · cited by 25,697
- Complexstatement and proof · cited by 5,565
- Real.pistatement and proof · cited by 1,774
- IsPrimitiveRootstatement and proof · cited by 356
- two_ne_zeroproof · cited by 251
- Complex.argstatement and proof · cited by 220
- Complex.arg_neg_oneproof · cited by 3
- IsPrimitiveRoot.neg_oneproof · cited by 3
- IsPrimitiveRoot.arg_extproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- Polynomial.cyclotomic_eval_lt_add_one_pow_totientproof · cited by 1