Theorems · Theorem · number theory
ZMod.card_units_eq_totient
∀ (n : ℕ) [NeZero n] [inst : Fintype (ZMod n)ˣ], Fintype.card (ZMod n)ˣ = n.totient
Note this takes an explicit Fintype ((ZMod n)ˣ) argument to avoid trouble with instance
diamonds.
- Defined in
- Mathlib.Data.Nat.Totient
- Cited by
- 15 results in Mathlib
- Foundations
- Depth 80 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites17
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Fintypestatement and proof · cited by 7,736
- Finset.sumproof · cited by 5,195
- Finset.univproof · cited by 3,473
- Unitsstatement and proof · cited by 2,804
- Finset.cardproof · cited by 2,327
- Fintype.cardstatement · cited by 1,386
- Finset.rangeproof · cited by 1,341
- ZModstatement and proof · cited by 1,024
- Finset.filterproof · cited by 949
- Finset.filter_congrproof · cited by 167
- ZMod.valproof · cited by 159
- Nat.totientstatement · cited by 111
Cited by15
Results whose statement or proof uses this declaration.
- Nat.totient_evenproof · cited by 4
- ZMod.not_isCyclic_units_eightproof · cited by 2
- Nat.prime_iff_card_unitsproof · cited by 2
- ZMod.isCyclic_units_of_prime_powproof · cited by 2
- Nat.card_units_zmod_lt_sub_oneproof · cited by 1
- ZMod.not_isCyclic_units_of_mul_coprimeproof · cited by 1
- ZMod.isCyclic_units_four_mul_iffproof · cited by 1
- IsCyclic.card_mulAutproof · cited by 1
- ArithmeticFunction.carmichael_two_pow_of_le_two_eq_totientproof · cited by 1
- ArithmeticFunction.carmichael_two_pow_of_ne_twoproof · cited by 1
- ZMod.pow_totientproof · cited by 1
- DirichletCharacter.card_eq_totient_of_hasEnoughRootsOfUnityproof · cited by 1