Theorems · Theorem · number theory
padicValNat_factorial_mul
∀ {p : ℕ} (n : ℕ) [hp : Fact (Nat.Prime p)], padicValNat p (p * n).factorial = padicValNat p n.factorial + nThe p-adic valuation of (p * n)! is n more than that of n!.
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- Foundations
- Depth 80 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Fact
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- ENatproof · cited by 4,985
- Factstatement and proof · cited by 2,726
- Nat.Primestatement and proof · cited by 2,059
- Nat.factorialstatement and proof · cited by 616
- Nat.cast_addproof · cited by 586
- Fact.outproof · cited by 328
- emultiplicityproof · cited by 156
- padicValNatstatement and proof · cited by 106
- Nat.factorial_ne_zeroproof · cited by 56
- Nat.cast_injectiveproof · cited by 39
- padicValNat_eq_emultiplicityproof · cited by 9
- Nat.Prime.emultiplicity_factorial_mulproof · cited by 3
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