Theorems · Theorem · number theory
Nat.Prime.eq_one_or_self_of_dvd
∀ {p : ℕ}, Nat.Prime p → ∀ (m : ℕ), m ∣ p → m = 1 ∨ m = p- Defined in
- Mathlib.Data.Nat.Prime.Defs
- Cited by
- 11 results in Mathlib
- Foundations
- Depth 22 from the axioms · uses propext
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- mul_oneproof · cited by 3,885
- Nat.Primestatement and proof · cited by 2,059
- IsUnitproof · cited by 1,602
- Irreducible.isUnit_or_isUnitproof · cited by 28
- Nat.isUnit_iffproof · cited by 7
Cited by11
Results whose statement or proof uses this declaration.
- Nat.dvd_primeproof · cited by 18
- Nat.Prime.eq_two_or_oddproof · cited by 6
- Nat.prime_defproof · cited by 3
- Equiv.Perm.pow_prime_eq_one_iffproof · cited by 2
- Nat.not_prime_of_dvd_of_neproof · cited by 2
- Nat.Prime.sum_four_squaresproof · cited by 1
- Equiv.Perm.cycleType_prime_orderproof · cited by 1
- Nat.prime_of_pow_sub_one_primeproof · cited by 1
- Subalgebra.isSimpleOrder_of_finrank_primeproof · cited by 0
- CharP.cast_ne_zero_of_ne_of_primeproof · cited by 0
- MixedCharZero.reduce_to_maximal_idealproof · cited by 0