Random number generator RNG, RAN0

To see how this works we note first that $$\begin{equation} (aN_{i-1}) \mathrm{MOD} (M)= (aN_{i-1}-[N_{i-1}/q]M)\mathrm{MOD} (M), \tag{16} \end{equation}$$ since we can add or subtract any integer multiple of $M$ from $aN_{i-1}$. The last term $[N_{i-1}/q]M\mathrm{MOD}(M)$ is zero since the integer division $[N_{i-1}/q]$ just yields a constant which is multiplied with $M$.