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

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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/}
}
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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/