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12 votes
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Quadratic reciprocity for three primes?

The quadratic reciprocity law states that for $p_1\ne p_2$ prime, the product $\left(\frac{p_1}{p_2}\right)\left(\frac{p_2}{p_1}\right)$ takes values $1$ or $-1$ depending on whether $p_1$ and $p_2$ s …
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8 votes
1 answer
1k views

Biquadratic reciprocity for $p\equiv 1\pmod 4$ and $q\equiv 3\pmod 4$

For a prime $p\equiv 1\pmod 4$, let $\left(\frac{\cdot}{p}\right)_4$ denote the rational biquadratic residue symbol; that is, $$ \left(\frac{a}{p}\right)_4 = \begin{cases} \ \ \ …
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