Theorems · Theorem · number theory
Nat.ordCompl_eq_self_iff_zero_or_not_dvd
∀ (n : ℕ) {p : ℕ}, Nat.Prime p → (n / p ^ n.factorization p = n ↔ n = 0 ∨ ¬p ∣ n)- Defined in
- Mathlib.Data.Nat.Factorization.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 96 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Finsuppstatement · cited by 5,255
- Nat.Primestatement and proof · cited by 2,059
- pow_zeroproof · cited by 1,094
- Nat.factorizationstatement and proof · cited by 215
- Nat.factorization_zeroproof · cited by 32
- Nat.not_dvd_ordComplproof · cited by 4
- Nat.factorization_eq_zero_of_not_dvdproof · cited by 4
Cited by2
Results whose statement or proof uses this declaration.
- Nat.ordCompl_pow_mul_eq_self_iffproof · cited by 0
- Nat.ordCompl_pow_mul_of_not_dvdproof · cited by 0