Random number generator RNG

The most common random number generators are based on so-called Linear congruential relations of the type $$ \begin{equation*} N_i=(aN_{i-1}+c) \mathrm{MOD} (M), \end{equation*} $$ which yield a number in the interval [0,1] through $$ \begin{equation*} x_i=N_i/M \end{equation*} $$

The number \( M \) is called the period and it should be as large as possible and \( N_0 \) is the starting value, or seed. The function \( \mathrm{MOD} \) means the remainder, that is if we were to evaluate \( (13)\mathrm{MOD}(9) \), the outcome is the remainder of the division \( 13/9 \), namely \( 4 \).