Geodesic
Zolotarev's proof of Gauss reciprocity and Jacobi symbols
Serdica Mathematical Journal, Tome 37 (2011) no. 3, pp. 251-260.

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We extend to the Jacobi symbol Zolotarev's idea that the Legendre symbol is the sign of a permutation, which leads to simple, strightforward proofs of many results, the proof of the Gauss Reciprocity for Jacobi symbols including.
Keywords: Jacobi Symbol, Gauss Reciprocity, Permutations 
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     title = {Zolotarev's proof of {Gauss} reciprocity and {Jacobi} symbols},
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Szyjewski, Marek. Zolotarev's proof of Gauss reciprocity and Jacobi symbols. Serdica Mathematical Journal, Tome 37 (2011) no. 3, pp. 251-260. http://geodesic.mathdoc.fr/item/SMJ2_2011_37_3_a5/