Theorems · Theorem · number theory
Nat.dvd_prime
∀ {p m : ℕ}, Nat.Prime p → (m ∣ p ↔ m = 1 ∨ m = p)- Defined in
- Mathlib.Data.Nat.Prime.Defs
- Cited by
- 18 results in Mathlib
- Foundations
- Depth 23 from the axioms · uses propext
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
- dvd_rflproof · cited by 80
- one_dvdproof · cited by 37
- Nat.Prime.eq_one_or_self_of_dvdproof · cited by 11
Cited by18
Results whose statement or proof uses this declaration.
- Ring.two_ne_zeroproof · cited by 5
- isCyclic_of_card_dvd_primeproof · cited by 4
- Nat.prime_def_minFacproof · cited by 4
- Function.minimalPeriod_eq_prime_iffproof · cited by 3
- Subgroup.eq_bot_or_eq_top_of_prime_cardproof · cited by 3
- Nat.dvd_prime_two_leproof · cited by 3
- Nat.Prime.divisorsproof · cited by 3
- CharP.ringChar_of_prime_eq_zeroproof · cited by 2
- AddSubgroup.eq_bot_or_eq_top_of_prime_cardproof · cited by 2
- neg_one_eq_one_iffproof · cited by 2
- alternatingGroup.exponent_kleinFour_of_card_eq_fourproof · cited by 1
- Nat.coprime_fermatNumber_fermatNumberproof · cited by 1