Theorems · Theorem · number theory
Nat.totient_pos
∀ {n : ℕ}, 0 < n.totient ↔ 0 < n- Defined in
- Mathlib.Data.Nat.Totient
- Cited by
- 14 results in Mathlib
- Foundations
- Depth 62 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites1
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Nat.totientstatement · cited by 111
Cited by14
Results whose statement or proof uses this declaration.
- Nat.totient_mul_of_prime_of_dvdproof · cited by 4
- Polynomial.degree_cyclotomic_posproof · cited by 2
- ArithmeticFunction.vonMangoldt.residueClass_applyproof · cited by 2
- Nat.eq_or_eq_of_totient_eq_totientproof · cited by 2
- card_orderOf_eq_totient_aux₂proof · cited by 2
- card_addOrderOf_eq_totient_aux₂proof · cited by 2
- Nat.prod_primeFactors_pow_totient_ediv_dvdproof · cited by 2
- Polynomial.sub_one_lt_natAbs_cyclotomic_evalproof · cited by 1
- IsPrimitiveRoot.dvd_of_isCyclotomicExtensionproof · cited by 1
- ArithmeticFunction.vonMangoldt.LSeries_residueClass_eqproof · cited by 1
- Nat.dvd_two_of_totient_le_oneproof · cited by 1
- Polynomial.sub_one_pow_totient_lt_natAbs_cyclotomic_evalproof · cited by 1