Theorems · Theorem · number theory
Nat.totient_mul
∀ {m n : ℕ}, m.Coprime n → (m * n).totient = m.totient * n.totient- Defined in
- Mathlib.Data.Nat.Totient
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 86 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Unitsproof · cited by 2,804
- MulZeroClass.mul_zeroproof · cited by 2,091
- MulZeroClass.zero_mulproof · cited by 1,625
- Fintype.cardproof · cited by 1,386
- ZModproof · cited by 1,024
- MulEquiv.toEquivproof · cited by 126
- Nat.totientstatement and proof · cited by 111
- Fintype.card_congrproof · cited by 67
- right_ne_zero_of_mulproof · cited by 38
- left_ne_zero_of_mulproof · cited by 27
- RingEquiv.toMulEquivproof · cited by 26
- Fintype.card_prodproof · cited by 19
Cited by5
Results whose statement or proof uses this declaration.
- Nat.eq_or_eq_of_totient_eq_totientproof · cited by 2
- Nat.totient_eq_prod_factorizationproof · cited by 2
- Polynomial.cyclotomic_expand_eq_cyclotomic_mulproof · cited by 2
- IsCyclotomicExtension.Rat.discrproof · cited by 1
- Nat.totient_mul_of_prime_of_not_dvdproof · cited by 1