Diskretnaya Matematika, Tome 14 (2002) no. 2, pp. 20-32
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M. V. Larin. Transitive polynomial transformations of residue class rings. Diskretnaya Matematika, Tome 14 (2002) no. 2, pp. 20-32. http://geodesic.mathdoc.fr/item/DM_2002_14_2_a2/
@article{DM_2002_14_2_a2,
author = {M. V. Larin},
title = {Transitive polynomial transformations of residue class rings},
journal = {Diskretnaya Matematika},
pages = {20--32},
year = {2002},
volume = {14},
number = {2},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/DM_2002_14_2_a2/}
}
TY - JOUR
AU - M. V. Larin
TI - Transitive polynomial transformations of residue class rings
JO - Diskretnaya Matematika
PY - 2002
SP - 20
EP - 32
VL - 14
IS - 2
UR - http://geodesic.mathdoc.fr/item/DM_2002_14_2_a2/
LA - ru
ID - DM_2002_14_2_a2
ER -
%0 Journal Article
%A M. V. Larin
%T Transitive polynomial transformations of residue class rings
%J Diskretnaya Matematika
%D 2002
%P 20-32
%V 14
%N 2
%U http://geodesic.mathdoc.fr/item/DM_2002_14_2_a2/
%G ru
%F DM_2002_14_2_a2
We give a complete description of the polynomials $f(x)$ with integer coefficients such that the period of the recurring sequence $u_{i+1}\equiv f(u_i)\pmod m$ is equal to $m$.
[1] Knuth D. E., The art of computer programming. Seminumerical algorithms, vol. 2, Addison–Wesley, Reading, MA, 1981 | MR
[2] Nobauer W., “Zur Theorie der Polinomtransformationen und Permutationspolynome”, Math. Ann., 157:4 (1964), 332–342 | DOI | MR
[3] Singmaster D., “On polynomial functions $\operatorname{mod}m$”, J. Number Theory, 6:5 (1974), 345–352 | DOI | MR | Zbl
[4] Keller G., Olson F. R., “Counting polynomials functions $\operatorname{mod}p^n$”, Duke Math. J., 35:4 (1968), 835–838 | DOI | MR | Zbl
[5] Anashin V. S., “Uniformly distributed sequences in computer algebra, or how to construct program generators of random numbers”, J. Math. Sci., 89:4 (1998), 1355–1390 | DOI | MR | Zbl
