On a Periodic Property of Pseudo-Random Sequences

When 6 is defined in this way, a is said to belong to the exponent 6 modulo n. I t has been suggested by Lehmer [7] that , provided 6 is reasonably large, the numbers u,n -1 m a y be used as uniform variates in the range (0 --~ 1). In section 1 we shall give a general method for evaluating 6 and in section 2 the results of some of the well-known tests for randomness performed on digits generated by this multiplicative congruence method when the multiplier a is chosen to be 3 TM in order to give a sequence of maximum period for n = 10'.