Theorems · Theorem · number theory
Even.neg_one_pow
∀ {α : Type u_2} [inst : Monoid α] [inst_1 : HasDistribNeg α] {n : ℕ}, Even n → (-1) ^ n = 1- Defined in
- Mathlib.Algebra.Ring.Parity
- Cited by
- 20 results in Mathlib
- Foundations
- Depth 24 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
- Evenstatement and proof · cited by 444
- HasDistribNegstatement and proof · cited by 114
- Even.neg_powproof · cited by 99
Cited by20
Results whose statement or proof uses this declaration.
- bernoulli_eq_bernoulli'_of_ne_oneproof · cited by 10
- quadraticChar_neg_oneproof · cited by 5
- neg_one_pow_eq_iteproof · cited by 5
- IsCyclotomicExtension.discr_prime_pow_ne_twoproof · cited by 4
- neg_one_geom_sumproof · cited by 4
- IsPrimitiveRoot.sub_one_norm_eq_eval_cyclotomicproof · cited by 3
- FormalMultilinearSeries.ofScalars_comp_neg_idproof · cited by 3
- IsPrimitiveRoot.norm_eq_oneproof · cited by 3
- AlternatingGroup.map_subtype_of_cycleTypeproof · cited by 3
- LSeries.iteratedDeriv_alternatingproof · cited by 2
- AlternatingMap.neg_one_pow_smul_map_insertNthproof · cited by 2
- Equiv.Perm.OnCycleFactors.odd_of_centralizer_le_alternatingGroupproof · cited by 2