Theorems · Theorem · number theory
legendreSym.eq_zero_iff
∀ (p : ℕ) [inst : Fact (Nat.Prime p)] (a : ℤ), legendreSym p a = 0 ↔ ↑a = 0
The Legendre symbol of p and a is zero iff p ∣ a.
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 145 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.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Factstatement and proof · cited by 2,726
- Nat.Primestatement and proof · cited by 2,059
- ZModstatement · cited by 1,024
- legendreSymstatement · cited by 51
- quadraticChar_eq_zero_iffproof · cited by 1
Cited by3
Results whose statement or proof uses this declaration.
- jacobiSym.eq_zero_iff_not_coprimeproof · cited by 3
- legendreSym.quadratic_reciprocity'proof · cited by 3
- legendreSym.eq_zero_mod_of_eq_neg_oneproof · cited by 1