A non-linear congruential pseudo random number generator

A non-linear congruential pseudo random number generator is introduced. This generator does not have the lattice structure in the distribution of tuples of consecutive pseudo random numbers which appears in the case of linear congruential generators. A theorem on the period length of sequences produced by this type of generators is proved. This theorem justifies an algorithm to determine the period length. Finally a simulation problem is described where a linear congruential generator produces completely useless results whereas good results are obtained if a non-linear congruential generator of about the same period length is applied.