Theorems · Theorem · number theory
ZMod.nonsquare_of_jacobiSym_eq_neg_one
∀ {a : ℤ} {b : ℕ}, jacobiSym a b = -1 → ¬IsSquare ↑aIf J(a | b) is -1, then a is not a square modulo b.
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 149 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- ZModstatement and proof · cited by 1,024
- sqproof · cited by 280
- IsSquarestatement and proof · cited by 132
- Int.cast_mulproof · cited by 113
- sq_nonnegproof · cited by 106
- jacobiSymstatement and proof · cited by 44
- ZMod.valMinAbsproof · cited by 28
- ZMod.coe_valMinAbsproof · cited by 8
- jacobiSym.mod_leftproof · cited by 3
- jacobiSym.pow_leftproof · cited by 3
- ZMod.intCast_eq_intCast_iff'proof · cited by 3
Cited by0
Results whose statement or proof uses this declaration.
Nothing cites this yet.