Geodesic
Transitive polynomial transformations of residue class rings
Diskretnaya Matematika, Tome 14 (2002) no. 2, pp. 20-32.

Voir la notice de l'article provenant de la source Math-Net.Ru

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 $m$. 
@article{DM_2002_14_2_a2,
     author = {M. V. Larin},
     title = {Transitive polynomial transformations of residue class rings},
     journal = {Diskretnaya Matematika},
     pages = {20--32},
     publisher = {mathdoc},
     volume = {14},
     number = {2},
     year = {2002},
     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
PB  - mathdoc
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
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DM_2002_14_2_a2/
%G ru
%F DM_2002_14_2_a2
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/

[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