# Linear Congruential Generators

• Shu Tezuka
Chapter
Part of the The Springer International Series in Engineering and Computer Science book series (SECS, volume 315)

## Abstract

The linear congruential method is the most popular algorithm for random number generation in the field of computer simulations.The linear congruential generator (LCG) is defined by
$$\begin{array}{*{20}{c}} {{X_n} = a{X_{n - 1}} + c(modM),} \\ {{u_n} = \frac{{{X_n}}}{M},} \end{array}$$
where a, c, and M are integers and Xn,n=1,2,...,is a sequence of integers with $$0 \leqslant {X_n} < M$$. The normalized sequence un, n =1,2,...,is a random number sequence in [0, 1). The following results tell us how to choose the parameters a, c, and M to obtain the maximal period lengths.

## Keywords

Lattice Structure Period Length Primitive Root Chinese Remainder Theorem Short Vector
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.