Theorems · Theorem · number theory
neg_one_pow_eq_neg_one_iff_odd
∀ {R : Type u_4} [inst : Monoid R] [inst_1 : HasDistribNeg R] {n : ℕ}, -1 ≠ 1 → ((-1) ^ n = -1 ↔ Odd n)- Defined in
- Mathlib.Algebra.Ring.Parity
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 71 from the axioms · uses propext, Classical.choice, Quot.sound
- 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
- Evenproof · cited by 444
- Oddstatement and proof · cited by 364
- HasDistribNegstatement and proof · cited by 114
- neg_one_pow_eq_iteproof · cited by 5
Cited by1
Results whose statement or proof uses this declaration.
- Polynomial.Chebyshev.eval_T_real_eq_neg_one_iffproof · cited by 3