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Quadratic Reciprocity Relations


$\displaystyle \left({-1\over p}\right)$ $\textstyle =$ $\displaystyle (-1)^{(p-1)/2}$ (1)
$\displaystyle \left({2\over p}\right)$ $\textstyle =$ $\displaystyle (-1)^{(p^2-1)/8}$ (2)
$\displaystyle \left({q\over p}\right)$ $\textstyle =$ $\displaystyle \left({p\over q}\right)(-1)^{[(p-1)/2][(q-1)/2]},$ (3)

where $\left({{\textstyle{p\over q}}}\right)$ is the Legendre Symbol.

See also Quadratic Reciprocity Theorem




© 1996-9 Eric W. Weisstein
1999-05-25