Theorems · Theorem · number theory
FiniteField.isSquare_odd_prime_iff
∀ {F : Type u_1} [inst : Field F] [inst_1 : Fintype F],
ringChar F ≠ 2 →
∀ {p : ℕ} [inst_2 : Fact (Nat.Prime p)],
p ≠ 2 → (IsSquare ↑p ↔ (quadraticChar (ZMod p)) (↑(ZMod.χ₄ ↑(Fintype.card F)) * ↑(Fintype.card F)) ≠ -1)An odd prime p is a square in F iff the quadratic character of ZMod p does not
take the value -1 on χ₄#F * #F.
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 224 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites25
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Fintypestatement and proof · cited by 7,736
- Fieldstatement and proof · cited by 7,404
- Factstatement and proof · cited by 2,726
- MulZeroClass.mul_zeroproof · cited by 2,091
- Nat.Primestatement and proof · cited by 2,059
- Fintype.cardstatement and proof · cited by 1,386
- eq_or_neproof · cited by 1,117
- ZModstatement and proof · cited by 1,024
- PNatproof · cited by 392
- zero_powproof · cited by 361
- CharP.cast_eq_zeroproof · cited by 357
Cited by0
Results whose statement or proof uses this declaration.
Nothing cites this yet.