Theorems · Theorem · number theory
Nat.factorization_mul_apply_of_coprime
∀ {p a b : ℕ}, a.Coprime b → (a * b).factorization p = a.factorization p + b.factorization pFor coprime a and b, the power of p in a * b is the sum of the powers in a and b
- Defined in
- Mathlib.Data.Nat.Factorization.Defs
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 90 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Finsuppstatement · cited by 5,255
- Nat.factorizationstatement · cited by 215
- Nat.primeFactorsListproof · cited by 105
- Nat.perm_primeFactorsList_mul_of_coprimeproof · cited by 2
Cited by3
Results whose statement or proof uses this declaration.
- alternatingGroup.card_two_sylow_of_card_eq_fourproof · cited by 2
- Nat.factorization_eq_of_coprime_leftproof · cited by 1
- Nat.factorization_mul_of_coprimeproof · cited by 1