Theorems · Theorem · number theory
legendreSym.at_neg_one
∀ {p : ℕ} [inst : Fact (Nat.Prime p)], p ≠ 2 → legendreSym p (-1) = ZMod.χ₄ ↑plegendreSym p (-1) is given by χ₄ p.
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 146 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Fact
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
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
- Factstatement and proof · cited by 2,726
- Nat.Primestatement and proof · cited by 2,059
- ZModstatement and proof · cited by 1,024
- Int.cast_oneproof · cited by 371
- Int.cast_negproof · cited by 224
- MulCharstatement · cited by 186
- legendreSymstatement · cited by 51
- ZMod.cardproof · cited by 36
- quadraticCharproof · cited by 34
- ZMod.χ₄statement and proof · cited by 27
- ZMod.ringChar_zmod_nproof · cited by 9
Cited by2
Results whose statement or proof uses this declaration.
- jacobiSym.at_neg_oneproof · cited by 2
- legendreSym.at_negproof · cited by 0