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Theorems · Theorem · number theory

jacobiSym.ne_zero

∀ {a : ℤ} {b : ℕ}, a.gcd ↑b = 1 → jacobiSym a b ≠ 0

The symbol J(a | b) is nonzero when a and b are coprime.

Defined in
Mathlib.NumberTheory.LegendreSymbol.JacobiSymbol
Cited by
2 results in Mathlib
Foundations
Depth 160 from the axioms · uses propext, Classical.choice, Quot.sound
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

jacobiSym.eq_one_or_neg_one · cited by 1jacobiSym.eq_one_or_neg_o…jacobiSym.eq_zero_iff · cited by 0jacobiSym.eq_zero_iffone_ne_zero · cited by 885one_ne_zerojacobiSym · cited by 44jacobiSymeq_zero_or_neZero · cited by 36eq_zero_or_neZerojacobiSym.zero_right · cited by 4jacobiSym.zero_rightjacobiSym.eq_zero_iff_not_coprime · cited by 3jacobiSym.eq_zero_iff_not…jacobiSym.ne_zeroCITED BYCITES

Cites5

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Cited by2

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