Theorems · Theorem · number theory
Nat.dvd_prod_primeFactors_pow_self
∀ {n : ℕ}, n ≠ 0 → n ∣ (∏ p ∈ n.primeFactors, p) ^ n- Defined in
- Mathlib.Data.Nat.Factorization.Basic
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 92 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Finset.prodstatement and proof · cited by 2,356
- le_reflproof · cited by 2,061
- le_imp_le_of_le_of_leproof · cited by 576
- Nat.factorizationproof · cited by 215
- Nat.primeFactorsstatement and proof · cited by 129
- pow_dvd_powproof · cited by 56
- Nat.prime_of_mem_primeFactorsproof · cited by 29
- Finset.prod_powproof · cited by 10
- Finset.prod_dvd_prod_of_dvdproof · cited by 8
- Nat.factorization_defproof · cited by 4
- Nat.prod_primeFactors_pow_factorizationproof · cited by 2
Cited by4
Results whose statement or proof uses this declaration.
- Nat.dvd_pow_self_iffproof · cited by 2
- Nat.dvd_radical_pow_selfproof · cited by 0
- isPGroup_iff_isPGroup_prod_primeFactorsproof · cited by 0
- isPGroup_iff_primeFactors_card_subsetproof · cited by 0