Theorems · Theorem · number theory
quadraticChar_card_sqrts
∀ {F : Type u_1} [inst : Field F] [inst_1 : Fintype F] [inst_2 : DecidableEq F],
ringChar F ≠ 2 → ∀ (a : F), ↑{x | x ^ 2 = a}.toFinset.card = (quadraticChar F) a + 1The number of solutions to x^2 = a is determined by the quadratic character.
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 150 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- FieldFintypeDecidableEq
Around this declaration
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Cites32
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
- Setstatement · cited by 53,352
- Finsetproof · cited by 13,712
- Fintypestatement and proof · cited by 7,736
- Fieldstatement and proof · cited by 7,404
- Set.Elemproof · cited by 7,166
- Set.ofPredstatement and proof · cited by 6,101
- Finset.univproof · cited by 3,473
- Nat.cast_oneproof · cited by 2,501
- Finset.cardstatement and proof · cited by 2,327
- Finset.extproof · cited by 565
- neg_add_cancelproof · cited by 256
Cited by1
Results whose statement or proof uses this declaration.
- legendreSym.card_sqrtsproof · cited by 0