Theorems · Theorem · number theory
quadraticChar_dichotomy
∀ {F : Type u_1} [inst : Field F] [inst_1 : Fintype F] [inst_2 : DecidableEq F] {a : F},
a ≠ 0 → (quadraticChar F) a = 1 ∨ (quadraticChar F) a = -1The quadratic character is 1 or -1 on nonzero arguments.
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 147 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.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Fintypestatement and proof · cited by 7,736
- Fieldstatement and proof · cited by 7,404
- MulCharstatement · cited by 186
- quadraticCharstatement · cited by 34
- sq_eq_one_iffproof · cited by 14
- quadraticChar_sq_oneproof · cited by 3
Cited by3
Results whose statement or proof uses this declaration.
- quadraticChar_isQuadraticproof · cited by 3
- quadraticChar_eq_neg_one_iff_not_oneproof · cited by 2
- legendreSym.eq_one_or_neg_oneproof · cited by 1