Theorems · Theorem · number theory
GaussianInt.prime_iff_mod_four_eq_three_of_nat_prime
∀ (p : ℕ) [Fact (Nat.Prime p)], Prime ↑p ↔ p % 4 = 3
A prime natural number is prime in ℤ[i] if and only if it is 3 mod 4
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 149 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Fact
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Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Factstatement and proof · cited by 2,726
- Nat.Primestatement and proof · cited by 2,059
- Primestatement · cited by 277
- GaussianIntstatement · cited by 37
- GaussianInt.mod_four_eq_three_of_nat_prime_of_primeproof · cited by 1
- GaussianInt.prime_of_nat_prime_of_mod_four_eq_threeproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- Nat.Prime.sq_add_sqproof · cited by 1