Theorems · Theorem · number theory
Nat.prod_pow_factorization_centralBinom
∀ (n : ℕ), ∏ p ∈ Finset.range (2 * n + 1), p ^ n.centralBinom.factorization p = n.centralBinom
The nth central binomial coefficient is the product of its prime factors, which are
at most 2n.
- Defined in
- Mathlib.Data.Nat.Choose.Factorization
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 95 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Finsuppstatement · cited by 5,255
- Finset.prodstatement · cited by 2,356
- Finset.rangestatement · cited by 1,341
- Nat.factorizationstatement · cited by 215
- Nat.centralBinomstatement · cited by 24
- Nat.prod_pow_factorization_chooseproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- centralBinom_factorization_smallproof · cited by 1