Home > IMO, Number theory, Olympiad, Problem Solving > Sum of integer parts and prime number

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

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