Theorems · Theorem · number theory
isPrimePow_nat_iff
∀ (n : ℕ), IsPrimePow n ↔ ∃ p k, Nat.Prime p ∧ 0 < k ∧ p ^ k = n
- Defined in
- Mathlib.Algebra.IsPrimePow
- Cited by
- 9 results in Mathlib
- Foundations
- Depth 77 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Nat.Primestatement · cited by 2,059
- Primeproof · cited by 277
- IsPrimePowstatement · cited by 77
Cited by9
Results whose statement or proof uses this declaration.
- isPrimePow_iff_factorization_eq_singleproof · cited by 1
- isPrimePow_nat_iff_bounded_logproof · cited by 1
- Nat.Coprime.isPrimePow_dvd_mulproof · cited by 1
- ArithmeticFunction.moebius_apply_isPrimePow_not_primeproof · cited by 0
- isPrimePow_iff_unique_prime_dvdproof · cited by 0
- isPrimePow_nat_iff_boundedproof · cited by 0
- Nat.squarefree_and_prime_pow_iff_primeproof · cited by 0
- exists_ordCompl_eq_one_iff_isPrimePowproof · cited by 0
- Choose.gcd_choose_eq_one_of_not_isPrimePowproof · cited by 0