Theorems · Theorem · number theory
IsPrimitiveRoot.ne_one
∀ {M : Type u_1} [inst : CommMonoid M] {k : ℕ} {ζ : M}, IsPrimitiveRoot ζ k → 1 < k → ζ ≠ 1- Cited by
- 7 results in Mathlib
- Foundations
- Depth 22 from the axioms · uses propext
- Assumes
- CommMonoid
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.
- CommMonoidstatement and proof · cited by 2,264
- pow_oneproof · cited by 894
- one_ne_zeroproof · cited by 885
- IsPrimitiveRootstatement and proof · cited by 356
- IsPrimitiveRoot.pow_ne_one_of_pos_of_ltproof · cited by 4
Cited by7
Results whose statement or proof uses this declaration.
- IsPrimitiveRoot.eq_neg_one_of_two_rightproof · cited by 5
- IsPrimitiveRoot.geom_sum_eq_zeroproof · cited by 2
- NumberField.InfinitePlace.IsPrimitiveRoot.nrRealPlaces_eq_zero_of_two_ltproof · cited by 2
- IsPrimitiveRoot.finite_quotient_span_sub_oneproof · cited by 1
- IsPrimitiveRoot.finite_quotient_toInteger_sub_oneproof · cited by 1
- IsPrimitiveRoot.sub_one_dvd_natCastproof · cited by 0
- IsPrimitiveRoot.sub_one_ne_zeroproof · cited by 0