Theorems · Theorem · number theory
Nat.factorization_choose_le_log
∀ {p n k : ℕ}, (n.choose k).factorization p ≤ Nat.log p nA logarithmic upper bound on the multiplicity of a prime in a binomial coefficient.
- Defined in
- Mathlib.Data.Nat.Choose.Factorization
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 101 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Finsuppstatement · cited by 5,255
- Nat.Primeproof · cited by 2,059
- Nat.choosestatement and proof · cited by 494
- Finset.Icoproof · cited by 450
- le_of_not_gtproof · cited by 430
- LE.le.trans_eqproof · cited by 328
- Nat.factorizationstatement and proof · cited by 215
- Nat.logstatement and proof · cited by 101
- Nat.choose_eq_zero_of_ltproof · cited by 35
- Nat.factorization_zeroproof · cited by 32
- Not.imp_symmproof · cited by 25
Cited by3
Results whose statement or proof uses this declaration.
- Nat.factorization_choose_le_oneproof · cited by 1
- Chebyshev.choose_dvd_lcmUptoproof · cited by 1
- Nat.pow_factorization_choose_leproof · cited by 1