Using one of the reciprocity laws evaluate the quadratic Gauss sum $G(2;p)$. Comparing with the formula $G(2;p)=(2|p)G(1;p)$ deduce that $(2|p)=(-1)^{(p^2-1)/8}$ if $p$ an odd prime.

From Apostol Chapter 9. I can't see what is meant by the initial hint of using one of the reciprocity laws.

-

$G(2;m)=S(4,m)=\sqrt{\frac p 4} \frac{1+i}{\sqrt 2} \overline{S(m,4)}$
What is $S(a,m)$? – JavaMan Nov 23 '11 at 17:41