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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.

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