Theorems · Theorem · number theory
legendreSym.at_neg
∀ {p : ℕ} [inst : Fact (Nat.Prime p)], p ≠ 2 → ∀ (a : ℤ), legendreSym p (-a) = ZMod.χ₄ ↑p * legendreSym p aThe value of the Legendre symbol at -a is χ₄ p times the value at a.
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- Foundations
- Depth 147 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Fact
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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 · cited by 1,024
- MulCharstatement · cited by 186
- legendreSymstatement and proof · cited by 51
- ZMod.χ₄statement and proof · cited by 27
- neg_eq_neg_one_mulproof · cited by 21
- legendreSym.at_neg_oneproof · cited by 2
- legendreSym.mulproof · cited by 2
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