Theorems · Theorem · number theory
Nat.prod_factorization_pow_eq_self
∀ {n : ℕ}, n ≠ 0 → (n.factorization.prod fun x1 x2 => x1 ^ x2) = n- Defined in
- Mathlib.Data.Nat.Factorization.Defs
- Cited by
- 22 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.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Finsuppproof · cited by 5,255
- Multiset.prodproof · cited by 528
- Multiset.ofListproof · cited by 290
- Finsupp.prodstatement and proof · cited by 231
- Nat.factorizationstatement · cited by 215
- Nat.primeFactorsListproof · cited by 105
- Multiset.toFinsuppproof · cited by 33
- Nat.prod_primeFactorsListproof · cited by 15
- Multiset.toFinsupp_toMultisetproof · cited by 4
- Nat.factorization_eq_primeFactorsList_multisetproof · cited by 2
Cited by22
Results whose statement or proof uses this declaration.
- Nat.factorization_le_iff_dvdproof · cited by 18
- Nat.factorizationLCMLeft_mul_factorizationLCMRightproof · cited by 2
- Nat.prod_primeFactors_pow_factorizationproof · cited by 2
- Real.log_nat_eq_sum_factorizationproof · cited by 1
- Nat.factorizationLCMLeft_dvd_leftproof · cited by 1
- Nat.lcmUpto_eq_prodproof · cited by 1
- Nat.factorizationLCMRight_dvd_rightproof · cited by 1
- Nat.eq_pow_of_factorization_eq_singleproof · cited by 1
- Nat.dvd_prod_pow_of_factorization_leproof · cited by 1
- Nat.prod_pow_factorization_chooseproof · cited by 1
- Nat.totient_mul_prod_primeFactorsproof · cited by 1
- Nat.ceilRoot_one_leftproof · cited by 0