Theorems · Theorem · number theory
Nat.mul_divisors_filter_prime_pow
∀ {a b : ℕ}, a.Coprime b → {d ∈ (a * b).divisors | IsPrimePow d} = {d ∈ a.divisors ∪ b.divisors | IsPrimePow d}- Defined in
- Mathlib.Data.Nat.Factorization.PrimePow
- 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.
Cites16
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Finsetstatement · cited by 13,712
- mul_oneproof · cited by 3,885
- MulZeroClass.mul_zeroproof · cited by 2,091
- eq_or_neproof · cited by 1,117
- Finset.filterstatement · cited by 949
- Finset.extproof · cited by 565
- Nat.divisorsstatement and proof · cited by 137
- IsPrimePowstatement and proof · cited by 77
- Finset.filter.congr_simpproof · cited by 47
- Finset.filter_emptyproof · cited by 23
- Nat.divisors_zeroproof · cited by 12
- Finset.empty_unionproof · cited by 8
Cited by1
Results whose statement or proof uses this declaration.
- ArithmeticFunction.vonMangoldt_sumproof · cited by 2