Theorems · Theorem · number theory
Nat.factorization_eq_of_coprime_left
∀ {p a b : ℕ}, a.Coprime b → p ∈ a.primeFactorsList → (a * b).factorization p = a.factorization pIf p is a prime factor of a then the power of p in a is the same that in a * b,
for any b coprime to a.
- Defined in
- Mathlib.Data.Nat.Factorization.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 91 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
- add_zeroproof · cited by 2,707
- Nat.factorizationstatement and proof · cited by 215
- Nat.primeFactorsListstatement and proof · cited by 105
- Nat.primeFactorsList_count_eqproof · cited by 11
- Nat.coprime_primeFactorsList_disjointproof · cited by 3
- Nat.factorization_mul_apply_of_coprimeproof · cited by 3
Cited by1
Results whose statement or proof uses this declaration.
- Nat.factorization_eq_of_coprime_rightproof · cited by 0