On the relation between units and Jacobi sums in Prime cyclotomic Fields.

Francisco Thaine

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The terms of the form 7kx² in the generalized Lucas sequence with parameters P and Q

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Let Vₙ(P,Q) denote the generalized Lucas sequence with parameters P and Q. For all odd relatively prime values of P and Q such that P² + 4Q > 0, we determine all indices n such that Vₙ(P,Q) = 7kx² when k|P. As an application, we determine all indices n such that the equation Vₙ = 21x² has solutions.

Zolotarev's proof of Gauss reciprocity and Jacobi symbols

Szyjewski, Marek (2011)

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2000 Mathematics Subject Classification: Primary 11A15. 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.