Theorems · Theorem · number theory
Nat.totient_prime
∀ {p : ℕ}, Nat.Prime p → p.totient = p - 1- Defined in
- Mathlib.Data.Nat.Totient
- Cited by
- 11 results in Mathlib
- Foundations
- Depth 79 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- one_mulproof · cited by 2,841
- Nat.Primestatement and proof · cited by 2,059
- pow_zeroproof · cited by 1,094
- pow_oneproof · cited by 894
- tsub_selfproof · cited by 154
- Nat.totientstatement and proof · cited by 111
- Nat.totient_prime_powproof · cited by 13
Cited by11
Results whose statement or proof uses this declaration.
- Nat.totient_twoproof · cited by 5
- Polynomial.cyclotomic_expand_eq_cyclotomic_mulproof · cited by 2
- IsCyclotomicExtension.Rat.associated_zeta_sub_one_pow_primeproof · cited by 1
- IsCyclotomicExtension.discr_odd_primeproof · cited by 1
- IsCyclotomicExtension.Rat.discrproof · cited by 1
- IsPrimitiveRoot.sum_eq_zero_iff_forall_eqproof · cited by 1
- cyclotomic_comp_X_add_one_isEisensteinAtproof · cited by 1
- Nat.totient_eq_iff_primeproof · cited by 1
- Nat.totient_mul_of_prime_of_not_dvdproof · cited by 1
- IsCyclotomicExtension.Rat.three_pidproof · cited by 0
- IsCyclotomicExtension.Rat.five_pidproof · cited by 0