Geodesic
Permutation polynomials over residue class rings
Prikladnaâ diskretnaâ matematika, no. 4 (2013), pp. 16-21

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Problems of finding inverse for a permutation polynomial over the ring $\mathbb Z_{p^k}$ for prime $p$ and any $k>1$ are studied. Necessary and sufficient conditions for two permutation polynomials to be inverse polynomials modulo prime power are found. Given a known inverse polynomial modulo $p^2$, a formula for inverse polynomial modulo $p^k$ is pointed. Given a pair of inverse polynomials modulo $p^k$, a method for constructing other such pairs is proposed.
Mots-clés : permutation polynomials, polynomial permutations.
Keywords: residue class rings 
@article{PDM_2013_4_a1,
     author = {A. V. Karpov},
     title = {Permutation polynomials over residue class rings},
     journal = {Prikladna\^a diskretna\^a matematika},
     pages = {16--21},
     publisher = {mathdoc},
     number = {4},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/PDM_2013_4_a1/}
}
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A. V. Karpov. Permutation polynomials over residue class rings. Prikladnaâ diskretnaâ matematika, no. 4 (2013), pp. 16-21. http://geodesic.mathdoc.fr/item/PDM_2013_4_a1/