MathNet 2002 — Part 01 Question 120

Let $p$ be an odd prime such that $p \equiv 1 \pmod 4$. Evaluate with reasons, $\sum_{k=1}^{\frac{p-1}{2}} \left\{ \frac{k^2}{p} \right\}$, where $\{x\} = x - [x]$, $[x]$ being the greatest integer not exceeding $x$.