Theorems · Theorem · number theory
quadraticChar_sq_one
∀ {F : Type u_1} [inst : Field F] [inst_1 : Fintype F] [inst_2 : DecidableEq F] {a : F},
a ≠ 0 → (quadraticChar F) a ^ 2 = 1The square of the quadratic character on nonzero arguments is 1.
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 146 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.
Cites8
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
- map_mulproof · cited by 1,137
- MulCharstatement · cited by 186
- pow_twoproof · cited by 150
- quadraticCharstatement and proof · cited by 34
- quadraticChar_sq_one'proof · cited by 2
Cited by3
Results whose statement or proof uses this declaration.
- quadraticChar_dichotomyproof · cited by 3
- legendreSym.sq_oneproof · cited by 1
- legendreSym.quadratic_reciprocityproof · cited by 1