A generator of pseudo-random numbers sequences with a very long period

We show how it is possible to choose, in an adequate manner, the parameters a, b, and m of the linear congruential generator, x n + 1 = ( a ⋅ x n + b ) mod ⁡ m in order to maximize the period of the generated series of pseudo-random numbers, in such a manner that the period obtained is close to the theoretical upper bound of m!.