Prove that ifcis odd, then $\displaystyle (\frac{2}{c}) = (-1)^{\frac{(c^{2}-1)}{8}}$.

I know I'm supposed to use the theorem that states $\displaystyle (\frac{2}{p}) = (-1)^{\frac{p^{2}-1}{8}}$, wherepis an odd prime. But I'm not confident that stating thatcis simply an odd prime is enough to satisfy this.