Theorems · Theorem · number theory
Nat.sum_primeFactors_gcd_add_sum_primeFactors_mul
∀ {β : Type u_1} [inst : AddCommMonoid β] (m n : ℕ) (f : ℕ → β),
(m.gcd n).primeFactors.sum f + (m * n).primeFactors.sum f = m.primeFactors.sum f + n.primeFactors.sum f- Defined in
- Mathlib.Data.Nat.Factorization.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 86 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AddCommMonoid
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Cites15
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Finsetproof · cited by 13,712
- AddCommMonoidstatement and proof · cited by 12,281
- Finset.sumstatement and proof · cited by 5,195
- add_zeroproof · cited by 2,707
- zero_addproof · cited by 2,366
- Finset.sum_congrproof · cited by 2,323
- MulZeroClass.mul_zeroproof · cited by 2,091
- MulZeroClass.zero_mulproof · cited by 1,625
- add_commproof · cited by 1,535
- eq_or_neproof · cited by 1,117
- Nat.primeFactorsstatement and proof · cited by 129
- Nat.primeFactors_zeroproof · cited by 11
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