Theorems · Definition · number theory
Nat.factorizationLCMLeft
ℕ → ℕ → ℕ
If a = ∏ pᵢ ^ nᵢ and b = ∏ pᵢ ^ mᵢ, then factorizationLCMLeft = ∏ pᵢ ^ kᵢ, where
kᵢ = nᵢ if mᵢ ≤ nᵢ and 0 otherwise. Note that the product is over the divisors of lcm a b,
so if one of a or b is 0 then the result is 1.
- Defined in
- Mathlib.Data.Nat.Factorization.Defs
- Cited by
- 15 results in Mathlib
- Foundations
- Depth 87 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Finsupp.prodproof · cited by 231
- Nat.factorizationproof · cited by 215
Cited by15
Results whose statement or proof uses this declaration.
- IsPrimitiveRoot.pow_mul_pow_lcmstatement and proof · cited by 4
- Nat.factorizationLCMLeft_mul_factorizationLCMRightstatement and proof · cited by 2
- Commute.orderOf_mul_pow_eq_lcmstatement and proof · cited by 2
- IsPrimitiveRoot.adjoin_pair_eqproof · cited by 1
- Nat.factorizationLCMLeft_dvd_leftstatement and proof · cited by 1
- IsCyclotomicExtension.lcm_supproof · cited by 1
- IsPrimitiveRoot.lcm_totient_le_finrankproof · cited by 1
- Nat.coprime_factorizationLCMLeft_factorizationLCMRightstatement · cited by 1
- AddCommute.addOrderOf_add_nsmul_eq_lcmstatement and proof · cited by 1
- AddCommute.exists_addOrderOf_eq_lcmproof · cited by 0
- Commute.exists_orderOf_eq_lcmproof · cited by 0
- IsCyclotomicExtension.Rat.torsionOrder_eqproof · cited by 0