Higher Powers
Generalizations of Gauss's lemma can be used to compute higher power residue symbols. In his second monograph on biquadratic reciprocity, Gauss used a fourth-power lemma to derive the formula for the biquadratic character of 1 + i in Z, the ring of Gaussian integers. Subsequently, Eisenstein used third- and fourth-power versions to prove cubic and quartic reciprocity.
Read more about this topic: Gauss's Lemma (number Theory)
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