Last time we took a look at pseudo random number generators, being

Specifically, we considered congruential generators which, starting from an initial value of

where is the remainder of integer division of

We saw that we needed to be careful with our choices of the values of

*entirely*deterministic sequences of numbers that pass many of the tests that we might use to try to identify truly random sequences.Specifically, we considered congruential generators which, starting from an initial value of

*x*_{0}, known as the*seed*, follow the rule*x*_{i+1}= (*a*×*x*_{i}+*c*) %*m*where

*x*%

*m*

*x*by*m*,*a*is known as the*multiplier*,*c*as the*increment*and*m*as the*modulus*.We saw that we needed to be careful with our choices of the values of

*a*,*c*,*m*and*x*_{0}if we wished to construct sequences that approximate randomness, not least that we should choose values for*a*,*c*and*x*_{0}that are strictly less than*m*, and the easiest way to do so is to simply copy those that have stood the test of time.Full text...