Theorems · Theorem · number theory
legendreSym.mul
∀ (p : ℕ) [inst : Fact (Nat.Prime p)] (a b : ℤ), legendreSym p (a * b) = legendreSym p a * legendreSym p b
The Legendre symbol is multiplicative in a for p fixed.
- Cited by
- 2 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.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Factstatement and proof · cited by 2,726
- Nat.Primestatement and proof · cited by 2,059
- map_mulproof · cited by 1,137
- ZModproof · cited by 1,024
- Int.cast_mulproof · cited by 113
- legendreSymstatement · cited by 51
- quadraticCharproof · cited by 34
- quadraticCharFunproof · cited by 9
- quadraticChar_applyproof · cited by 5
Cited by3
Results whose statement or proof uses this declaration.
- jacobiSym.mul_leftproof · cited by 8
- legendreSym.homproof · cited by 1
- legendreSym.at_negproof · cited by 0