Theorems · Theorem · number theory
jacobiSym.mul_left
∀ (a₁ a₂ : ℤ) (b : ℕ), jacobiSym (a₁ * a₂) b = jacobiSym a₁ b * jacobiSym a₂ b
The Jacobi symbol is multiplicative in its first argument.
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 146 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Nat.primeFactorsListproof · cited by 105
- legendreSymproof · cited by 51
- jacobiSymstatement · cited by 44
- Nat.prime_of_mem_primeFactorsListproof · cited by 30
- legendreSym.mulproof · cited by 2
- List.prod_map_mulproof · cited by 1
Cited by8
Results whose statement or proof uses this declaration.
- jacobiSym.pow_leftproof · cited by 3
- jacobiSym.quadratic_reciprocity'proof · cited by 2
- qrSign.mul_leftproof · cited by 1
- jacobiSym.mod_right'proof · cited by 1
- jacobiSym.negproof · cited by 1
- jacobiSym.div_four_leftproof · cited by 1
- jacobiSym.even_oddproof · cited by 0
- jacobiSym.list_prod_leftproof · cited by 0