### Abstract

We derive two different general relationships that exist among terms of the linear congruential generator x_{i}+_{1} = ax_{i} + b mod 2^{β} that are separated by powers of two. These two relationships are not equivalent except in one special case which turns out to be Marsaglia's result.

Original language | English (US) |
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Pages (from-to) | 381-383 |

Number of pages | 3 |

Journal | Statistics and Probability Letters |

Volume | 15 |

Issue number | 5 |

DOIs | |

State | Published - Dec 8 1992 |

### Keywords

- Monte Carlo simulation
- Random number generator
- linear congruential generator
- long range corelations

### ASJC Scopus subject areas

- Statistics and Probability
- Statistics, Probability and Uncertainty

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## Cite this

Percus, O. E., & Percus, J. K. (1992). Intrinsic relations in the structure of linear congruential generators modulo 2

^{β}.*Statistics and Probability Letters*,*15*(5), 381-383. https://doi.org/10.1016/0167-7152(92)90158-2