The period of pseudo-random numbers generated by Lehmer's congruential method

Abstract

Lehmer has given a congruential method for generating a sequence of pseudo-random numbers. A known technique is available for checking whether the period of the sequence is maximal. In the present note it is shown how to calculate the period, whether or not this is maximal. The procedure is applied to various cases of Lehmer's sequences and it is found that, contrary to previous assertions, certain cases do not have maximal period.The theory of Lehmer's sequences is also made more accessible for non-experts in number theory. © 1976 The British Computer Society.