A multiple recursive non-linear congruential pseudo random number generator
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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 .
KeywordsNumber Theory Algebraic Geometry Topological Group Period Length Pseudo Random Number
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- Beyer, W.A.; Roof, R.B. and Williamson, D.: The lattice structure of multiplicative pseudo-random vectors. Math. Comp. 25, 345–363 (1971)Google Scholar
- Eichenauer, J. and Lehn J.: A non-linear congruential pseudo random number generator. Statistical Papers (to appear 1986)Google Scholar
- Kowalsky, H.-J.: Lineare Algebra, 9th ed., de Gruyter, Berlin-New York (1979)Google Scholar
- Knuth, D.E.: The art of computer programming, vol. 2, 2nd ed., Addison-Wesley, Reading (1981)Google Scholar
- Marsaglia, G.: Random numbers fall mainly in the planes. Proc. Nat. Acad. Sci. 61, 25–28 (1968)Google Scholar