Abstract
When we study a congruence T(x) ≡ ax modulo m as pseudo random number generator, there are several means of ensuring the independence of two successive numbers. In this report, we show that the dependence depends on the continued fraction expansion of m/a. We deduce that the congruences such that m and a are two successive elements of Fibonacci sequences are those having the weakest dependence. We will use this result to obtain truly random number sequences xn. For that purpose, we will use non-deterministic sequences yn. They are transformed using Fibonacci congruences and we will get by this way sequences xn. These sequences xn admit the IID model for correct model.
Highlights
In this paper, we present a new method using Fibonacci sequences numbers1.to To obtain real IID sequences xn of have random number two methods random exists : 1) use of pseudo-random generators, 2) use of random noise.But, up to now no completely reliable solution had been proposed ([1]-[3])
When we study a congruence T(x) ≡ ax modulo m as pseudo random number generator, there are several means of ensuring the independence of two successive numbers
We show that the dependence depends on the continued fraction expansion of m/a
Summary
We present a new method using Fibonacci sequences numbers1. to To obtain real IID sequences xn of have random number two methods random exists : 1) use of pseudo-random generators (for example the linear congruence), 2) use of random noise To To obtain real IID sequences xn of have random number two methods random exists : 1) use of pseudo-random generators (for example the linear congruence), 2) use of random noise Up to now no completely reliable solution had been proposed ([1]-[3]). To set straight this situation, Marsaglia has created a Cd-Rom of random numbers by using sequences of numbers provided by Rap music. He has not proved that the sequence obtained is really random. One obtains sequence of real xnsuch that the IID model is a correct model of xn
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