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Mathematics-Online lexicon:

Maximum Period Length and the Linear Congruential Method

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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 $ m$ of $ \beta-1$.

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


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  automatically generated 12/ 7/2007