Theorems · Theorem · number theory
Nat.emultiplicity_eq_card_pow_dvd
∀ {m n b : ℕ}, m ≠ 1 → 0 < n → Nat.log m n < b → emultiplicity m n = ↑{i ∈ Finset.Ico 1 b | m ^ i ∣ n}.cardThe multiplicity of m in n is the number of positive natural numbers i such that m ^ i
divides n. This set is expressed by filtering Ico 1 b where b is any bound greater than
log m n.
- Defined in
- Mathlib.Data.Nat.Multiplicity
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 58 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites20
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- ENatstatement · cited by 4,985
- Finset.cardstatement and proof · cited by 2,327
- LT.lt.ne'proof · cited by 1,417
- Finset.filterstatement · cited by 949
- LE.le.trans_ltproof · cited by 795
- Finset.extproof · cited by 565
- Finset.Icostatement and proof · cited by 450
- zero_powproof · cited by 361
- add_tsub_cancel_rightproof · cited by 172
- Finset.filter_congrproof · cited by 167
- emultiplicitystatement · cited by 156
- multiplicityproof · cited by 117
Cited by1
Results whose statement or proof uses this declaration.
- Nat.Prime.emultiplicity_choose_prime_pow_add_emultiplicityproof · cited by 2