Theorems · Theorem · number theory
Nat.radical_eq_prod_primeFactors
∀ {n : ℕ}, UniqueFactorizationMonoid.radical n = ∏ p ∈ n.primeFactors, p- Defined in
- Mathlib.RingTheory.Radical.NatInt
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 80 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Finset.prodstatement and proof · cited by 2,356
- Finset.prod_congrproof · cited by 646
- Nat.primeFactorsstatement and proof · cited by 129
- UniqueFactorizationMonoid.radicalstatement · cited by 64
- UniqueFactorizationMonoid.primeFactors_eq_natPrimeFactorsproof · cited by 1
Cited by7
Results whose statement or proof uses this declaration.
- Nat.one_lt_radical_iffproof · cited by 3
- Int.radical_natAbs_eq_radicalproof · cited by 3
- Int.radical_eq_prod_primeFactorsproof · cited by 1
- Nat.dvd_radical_pow_selfproof · cited by 0
- Nat.primeFactors_radicalproof · cited by 0
- Nat.radical_dvd_iffproof · cited by 0
- Int.radical_natCastproof · cited by 0