Reciprocity Law - Quartic Reciprocity

Quartic Reciprocity

In terms of the quartic residue symbol, the law of quartic reciprocity for Gaussian integers states that if π and θ are primary (congruent to 1 mod (1+i)3) Gaussian primes then

\Bigg\left^{-1}=
(-1)^{\frac{N\pi - 1}{4}\frac{N\theta-1}{4}}.

Read more about this topic:  Reciprocity Law

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