Theorems · Theorem · number theory
Nat.eq_sq_add_sq_of_isSquare_mod_neg_one
∀ {n : ℕ}, IsSquare (-1) → ∃ x y, n = x ^ 2 + y ^ 2If -1 is a square modulo the natural number n, then n is a sum of two squares.
- Defined in
- Mathlib.NumberTheory.SumTwoSquares
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 151 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Factproof · cited by 2,726
- mul_commproof · cited by 2,262
- Nat.Primeproof · cited by 2,059
- ZModstatement · cited by 1,024
- IsSquarestatement and proof · cited by 132
- induction_on_primesproof · cited by 5
- ZMod.exists_sq_eq_neg_one_iffproof · cited by 4
- ZMod.isSquare_neg_one_of_dvdproof · cited by 2
- Nat.sq_add_sq_mulproof · cited by 1
- Nat.Prime.sq_add_sqproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- Nat.eq_sq_add_sq_iff_eq_sq_mulproof · cited by 1