Proving that for any odd integer: $\lceil \frac{N^2}{4} \rceil = \frac{N^2 + 3}{4}$ I'm trying to construct a proof that for any odd integer: the ceiling of $\large \lceil  \frac{N^2}{4} \rceil = \frac{N^2 + 3}{4}$.  
Anyone have a second to show me how this is done?  Thanks!

Take $N=2k+1$ then we have,
$(N^2+3)/4=k^2+k+1$
$N^2/4=k^2+k+1/4,\Rightarrow $ its ceiling is $\lceil N^2/4\rceil =k^2+k+1=(N^2+3)/4$
