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Fibonacci Congruences and Applications
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Open Journal of Statistics·Volume 01 (2011)·Pages 128–138·Published 12 July 2011·DOI10.4236/ojs.2011.12015
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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 x<sub>n</sub>. For that purpose, we will use non-deterministic sequences y<sub>n</sub>. They are transformed using Fibonacci congruences and we will get by this way sequences x<sub>n</sub>. These sequences x<sub>n</sub> admit the IID model for correct model.
KeywordsFibonacci SequenceLinear CongruenceRandom NumbersDependenceCorrect Models
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