Theorems · Theorem · number theory
Nat.factorization_eq_card_pow_dvd
∀ (n : ℕ) {p : ℕ}, Nat.Prime p → n.factorization p = {i ∈ Finset.Ico 1 n | p ^ i ∣ n}.card- Defined in
- Mathlib.Data.Nat.Factorization.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 95 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
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
- Finset.cardstatement and proof · cited by 2,327
- Nat.Primestatement and proof · cited by 2,059
- Finset.filterstatement · cited by 949
- Finset.Icostatement · cited by 450
- Nat.factorizationstatement and proof · cited by 215
- add_tsub_cancel_rightproof · cited by 172
- Nat.card_Iccproof · cited by 14
- Nat.Icc_factorization_eq_pow_dvdproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- Nat.factorization_eq_card_pow_dvd_of_ltproof · cited by 1