I do not know how to prove the following statement:
Let $p \equiv 7 \pmod 8$ be a prime. Then $$\sum\limits_{r = 1}^{\frac{p - 1}{2}}r \left( \frac{r}{p} \right) = 0$$ where $\left( \dfrac{\cdot}{\cdot} \right)$ is the Legendre symbol.
Could anybody help me to answer this question?