IMO Shortlist 1995 problem NC8
Dodao/la:
arhiva2. travnja 2012. Let
![p](/media/m/1/c/8/1c85c88d10b11745150467bf9935f7de.png)
be an odd prime. Determine positive integers
![x](/media/m/f/1/8/f185adeed9bd346bc960bca0147d7aae.png)
and
![y](/media/m/c/c/0/cc082a07a517ebbe9b72fd580832a939.png)
for which
![x \leq y](/media/m/d/3/d/d3dd97913bd3f7ddc264cd38b6393421.png)
and
![\sqrt{2p} - \sqrt{x} - \sqrt{y}](/media/m/1/0/9/109b7eba434ace27faa8d590cbd329d5.png)
is non-negative and as small as possible.
%V0
Let $p$ be an odd prime. Determine positive integers $x$ and $y$ for which $x \leq y$ and $\sqrt{2p} - \sqrt{x} - \sqrt{y}$ is non-negative and as small as possible.
Izvor: Međunarodna matematička olimpijada, shortlist 1995