Abstract
Let p, q, r be distinct rational primes. It is shown that the pth power residue symbol \({(q/r)_p = 1}\) over the pth cyclotomic field provided p is odd. This will be used for an elementary approach to the classical Eisenstein reciprocity law. We also examine when q is a pth power in \({\mathbb{F}_r^* = (\mathbb{Z}/r\mathbb{Z})^*}\).
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Schmid, P. On Eisenstein reciprocity. Arch. Math. 104, 343–346 (2015). https://doi.org/10.1007/s00013-015-0745-6
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DOI: https://doi.org/10.1007/s00013-015-0745-6