Theorems · Theorem · number theory
Nat.dvd_prime_pow
∀ {p : ℕ}, Nat.Prime p → ∀ {m i : ℕ}, i ∣ p ^ m ↔ ∃ k ≤ m, i = p ^ k- Defined in
- Mathlib.Data.Nat.Prime.Basic
- Cited by
- 13 results in Mathlib
- Foundations
- Depth 76 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Nat.Primestatement and proof · cited by 2,059
- Nat.prime_iffproof · cited by 20
- dvd_prime_powproof · cited by 6
- associated_eq_eqproof · cited by 6
Cited by13
Results whose statement or proof uses this declaration.
- IsPGroup.iff_cardproof · cited by 7
- Equiv.Perm.card_compl_support_modEqproof · cited by 3
- IsPGroup.iff_orderOfproof · cited by 2
- Nat.eq_prime_pow_of_dvd_least_prime_powproof · cited by 2
- exists_addOrderOf_eq_prime_pow_iffproof · cited by 2
- exists_orderOf_eq_prime_pow_iffproof · cited by 2
- isPGroup_iff_exponent_eq_powproof · cited by 1
- IsPGroup.indexproof · cited by 1
- Nat.mem_properDivisors_prime_powproof · cited by 1
- charP_of_prime_pow_injectiveproof · cited by 1
- Nat.mem_divisors_prime_powproof · cited by 1
- ArithmeticFunction.carmichael_two_pow_of_ne_twoproof · cited by 1