On the Jacobi Symbol Original Research Article

Frobenius suggested taking Zolotarev′s Theorem, which characterises the Legendre symbol, as the definition for the Jacobi symbol. We show that the theory of quadratic residues can be further simplified by following Zolotarev′s approach to reciprocity rather than proceeding by way of Gauss′s Lemma as Frobenius and later authors have done.