Theorems · Theorem · number theory
Odd.neg_one_pow
∀ {α : Type u_2} [inst : Monoid α] [inst_1 : HasDistribNeg α] {n : ℕ}, Odd n → (-1) ^ n = -1- Defined in
- Mathlib.Algebra.Ring.Parity
- Cited by
- 18 results in Mathlib
- Foundations
- Depth 26 from the axioms · uses propext
- Assumes
- MonoidHasDistribNeg
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Monoidstatement and proof · cited by 3,887
- one_powproof · cited by 521
- Oddstatement and proof · cited by 364
- HasDistribNegstatement and proof · cited by 114
- Odd.neg_powproof · cited by 14
Cited by18
Results whose statement or proof uses this declaration.
- quadraticChar_neg_oneproof · cited by 5
- neg_one_pow_eq_iteproof · cited by 5
- IsCyclotomicExtension.discr_prime_pow_ne_twoproof · cited by 4
- AlgebraicTopology.DoldKan.HigherFacesVanish.comp_Hσ_eqproof · cited by 4
- neg_one_geom_sumproof · cited by 4
- Int.fib_negproof · cited by 4
- FormalMultilinearSeries.ofScalars_comp_neg_idproof · cited by 3
- bernoulli'_eq_zero_of_oddproof · cited by 2
- Complex.hasSum_arctanproof · cited by 1
- IsCyclotomicExtension.discr_prime_pow_eq_unit_mul_powproof · cited by 1
- Equiv.Perm.sign_of_cycleType_eq_replicateproof · cited by 1
- Equiv.Perm.count_le_one_of_centralizer_le_alternatingproof · cited by 1