Theorems · Theorem · number theory
quadraticChar_neg_one_iff_not_isSquare
∀ {F : Type u_1} [inst : Field F] [inst_1 : Fintype F] [inst_2 : DecidableEq F] {a : F},
(quadraticChar F) a = -1 ↔ ¬IsSquare aFor a : F, quadraticChar F a = -1 ↔ ¬ IsSquare a.
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 149 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- FieldFintypeDecidableEq
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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
- MulCharstatement · cited by 186
- IsSquarestatement and proof · cited by 132
- quadraticCharstatement and proof · cited by 34
- MulChar.map_zeroproof · cited by 10
- quadraticChar_one_iff_isSquareproof · cited by 6
- quadraticChar_eq_neg_one_iff_not_oneproof · cited by 2
Cited by4
Results whose statement or proof uses this declaration.
- legendreSym.eq_neg_one_iffproof · cited by 2
- quadraticChar_exists_neg_oneproof · cited by 1
- quadraticChar_card_sqrtsproof · cited by 1
- FiniteField.isSquare_odd_prime_iffproof · cited by 0