Theorems · Theorem · number theory
Nat.prod_primeFactors_of_squarefree
∀ {n : ℕ}, Squarefree n → ∏ p ∈ n.primeFactors, p = n- Defined in
- Mathlib.Data.Nat.Squarefree
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 81 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Finsetproof · cited by 13,712
- Finset.prodstatement and proof · cited by 2,356
- Nat.primeFactorsstatement · cited by 129
- Squarefreestatement and proof · cited by 112
- Nat.primeFactorsListproof · cited by 105
- Squarefree.ne_zeroproof · cited by 18
- Nat.prod_primeFactorsListproof · cited by 15
- List.prod_toFinsetproof · cited by 3
- Nat.toFinset_factorsproof · cited by 3
- Squarefree.nodup_primeFactorsListproof · cited by 1
Cited by7
Results whose statement or proof uses this declaration.
- BoundingSieve.prod_primeFactors_nuproof · cited by 2
- Nat.prod_primeFactors_sdiff_of_squarefreeproof · cited by 1
- Nat.prod_primeFactors_invOn_squarefreeproof · cited by 1
- Nat.eq_prod_primes_mul_sq_of_mem_smoothNumbersproof · cited by 1
- Squarefree.dvd_primorialproof · cited by 0
- Nat.grahamConjecture_of_squarefreeproof · cited by 0
- ArithmeticFunction.IsMultiplicative.prod_primeFactorsproof · cited by 0