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## Sum of integer parts and prime number

Let $p$ be a prime such that $p \equiv 1(\text{mod } 4)$. Calculate the sum
$\displaystyle s=\left\lfloor \sqrt{1\cdot p}\right\rfloor + \left\lfloor \sqrt{2\cdot p}\right\rfloor+\cdots +\left\lfloor \sqrt{\frac{p-1}{4}\cdot p}\right\rfloor$.
IMO