Theorems · Theorem · number theory
IsPrimitiveRoot.pow_inj
∀ {M : Type u_1} [inst : CommMonoid M] {k : ℕ} {ζ : M},
IsPrimitiveRoot ζ k → ∀ ⦃i j : ℕ⦄, i < k → j < k → ζ ^ i = ζ ^ j → i = j- Cited by
- 4 results in Mathlib
- Foundations
- Depth 33 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommMonoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- one_mulproof · cited by 2,841
- CommMonoidstatement and proof · cited by 2,264
- le_antisymmproof · cited by 2,068
- lt_of_le_of_ltproof · cited by 432
- IsPrimitiveRootstatement and proof · cited by 356
- pow_addproof · cited by 315
- tsub_add_cancel_of_leproof · cited by 112
- le_of_not_geproof · cited by 72
- IsUnit.powproof · cited by 48
- tsub_eq_zero_iff_leproof · cited by 32
- tsub_le_selfproof · cited by 22
- IsPrimitiveRoot.isUnitproof · cited by 22
Cited by4
Results whose statement or proof uses this declaration.
- IsPrimitiveRoot.card_primitiveRootsproof · cited by 4
- IsPrimitiveRoot.injOn_powproof · cited by 1
- IsPrimitiveRoot.autToPow_eq_modularCyclotomicCharacterproof · cited by 0
- AddChar.zmodChar_primitive_of_primitive_rootproof · cited by 0