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, Volume 59, Issue 3, pp 331–346 | Cite as

A multiple recursive non-linear congruential pseudo random number generator

  • Jürgen Eichenauer
  • Holger Grothe
  • Jürgen Lehn
  • Alev Topuzoğlu
Article

Abstract

On-linear multiple recursive congruential pseudo random number generator with prime modulus p is introduced. Let x, n≥0, be the sequence generated by a usual linear (r+1)-step recursive congruential generator with prime modulus p and denote by N(n), n≥0, the sequence of non-negative integers with xN(n)≢0 (mod p). The non-linear generator is defined by zn≡xN(n)+1·x N(n) −1 (mod p), n≥0, where x N(n) −1 denotes the inverse element of xN(n) in the Galois field GF(p). A condition is given which ensures that the generated sequence is purely periodic with period length pr and all (p−1)r r-tupels (y1,...,yr) with 1≤y1,...,yr≤p are generated once per period when r-tupels of consecutive numbers of the generated sequence are formed. For r=1 this generator coincides with the generator introduced by Eichenauer and Lehn [2].

Keywords

Number Theory Algebraic Geometry Topological Group Period Length Pseudo Random Number 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

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    Eichenauer, J. and Lehn J.: A non-linear congruential pseudo random number generator. Statistical Papers (to appear 1986)Google Scholar
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    Marsaglia, G.: Random numbers fall mainly in the planes. Proc. Nat. Acad. Sci. 61, 25–28 (1968)Google Scholar

Copyright information

© Springer-Verlag 1987

Authors and Affiliations

  • Jürgen Eichenauer
    • 1
  • Holger Grothe
    • 1
  • Jürgen Lehn
    • 1
  • Alev Topuzoğlu
    • 2
  1. 1.Technische Hochschule Fachbereich MathematikDarmstadt
  2. 2.Department of MathematicsMiddle East Technical UniversityAnkaraTurkey

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