Cubic and Biquadratic Reciprocity
In Chapter 5 we saw that the law of quadratic reciprocity provided the answer to the question. For which primes p is the congruence x 2 ≡ a (p) solvable ? Here a is a fixed integer. If the same question is considered for congruences x n ≡ a (p), n a fixed positive integer, we are led into the realm of the higher reciprocity laws. When n = 3 and 4 we speak of cubic and biquadratic reciprocity.
KeywordsFinite Field Primary Element Residue Class Quadratic Residue Primary Complex
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