I am struggling with this proof. I really cannot think of where to start:
Let $p$ be an odd prime, prove that:
$$\left(\frac{1 \cdot 2}{p}\right) + \left(\frac{2 \cdot 3}{p}\right) + \left(\frac{3 \cdot 4}{p}\right) + \cdots + \left(\frac{(p - 2) (p - 1)}{p}\right) = -1$$
If someone could just give me a push in the right direction, I am sure I could get it.