Theorems · Theorem · number theory
Nat.Prime.dvd_choose_pow
∀ {p n k : ℕ}, Nat.Prime p → k ≠ 0 → k ≠ p ^ n → p ∣ (p ^ n).choose k- Defined in
- Mathlib.Data.Nat.Multiplicity
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 88 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.
- ENatproof · cited by 4,985
- zero_addproof · cited by 2,366
- LT.lt.leproof · cited by 2,189
- Nat.Primestatement and proof · cited by 2,059
- Nat.choosestatement and proof · cited by 494
- LT.lt.not_geproof · cited by 305
- emultiplicityproof · cited by 156
- Ne.bot_ltproof · cited by 116
- Ne.lt_or_gtproof · cited by 108
- Nat.choose_eq_zero_of_ltproof · cited by 35
- emultiplicity_eq_coeproof · cited by 9
- Nat.Prime.emultiplicity_choose_prime_pow_add_emultiplicityproof · cited by 2
Cited by3
Results whose statement or proof uses this declaration.
- Commute.add_pow_prime_pow_eq'proof · cited by 3
- Choose.minFac_dvd_gcd_choose_of_isPrimePowproof · cited by 2
- Nat.Prime.dvd_choose_pow_iffproof · cited by 0