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Results tagged with quadratic-reciprocity
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user 9924
8
votes
1
answer
1k
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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}
\ \ \ …
- 23k
12
votes
1
answer
835
views
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 …
- 23k