Mathematics-Online lexicon: Maximum Period Length and the Linear Congruential Method

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	Mathematics-Online lexicon:
	Maximum Period Length and the Linear Congruential Method

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overview

For a prime number $\beta$ , the sequence $\alpha^\ell\,$ mod $\,\beta$ , $\ell=0,1,\ldots$ , has exactly no period less than $\beta-1$ , if

$\displaystyle \alpha^{(\beta-1)/m} \ne 1\,$ mod $\displaystyle \,\beta$

for all prime divisors

of $\beta-1$ .

By applying this criterion, appropriate multipliers $\alpha$ can be determined for the simulation of random numbers by the linear congruential method.

Annotation:

Beweis: Maximale Periode bei der linearen Kongruenzmethode (german)

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automatically generated 12/ 7/2007