# Floor Function and Euler-Mascheroni Constant

I need to know how to express the following function, $\lfloor{\sqrt{c^2-707}}\rfloor^2=y$ $(s.t.$ $c$ and $y$ are in $N)$, analytically. I think http://mathworld.wolfram.com/Euler-MascheroniConstant.html, and https://en.wikipedia.org/wiki/Floor_and_ceiling_functions might help.