I have used mathematica to test following equation is true \begin{equation} \sum_{a,b=0}^{m-1} \left[\frac{a+b n}{m}\right] = \frac{n m^2}{2} -\frac{nm}{2} \end{equation} where $[x]$ is the floor function in mathematica

Do you have analytic derivation that how to get the RHS?

Thanks