Theorems · Theorem · number theory
Nat.Prime.sq_add_sq
- #20 of the 100 theorems: All Primes (1 mod 4) Equal the Sum of Two Squares
- 1000+ list: Fermat's theorem on sums of two squares
∀ {p : ℕ} [Fact (Nat.Prime p)], p % 4 ≠ 3 → ∃ a b, a ^ 2 + b ^ 2 = pFermat's theorem on the sum of two squares. Every prime not congruent to 3 mod 4 is the sum of two squares. Also known as Fermat's Christmas theorem.
- Defined in
- Mathlib.NumberTheory.SumTwoSquares
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 150 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Fact
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.
- Factstatement and proof · cited by 2,726
- Nat.Primestatement and proof · cited by 2,059
- irreducible_iff_primeproof · cited by 15
- GaussianInt.sq_add_sq_of_nat_prime_of_not_irreducibleproof · cited by 2
- GaussianInt.prime_iff_mod_four_eq_three_of_nat_primeproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- Nat.eq_sq_add_sq_of_isSquare_mod_neg_oneproof · cited by 1