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When Is the Number of True Different Permutation Polynomials Equal to 0?

Department of Telecommunications and Information Technologies, “Gheorghe Asachi” Technical University, Iasi 700506, Romania
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Mathematics 2019, 7(11), 1018; https://doi.org/10.3390/math7111018
Received: 31 July 2019 / Revised: 22 October 2019 / Accepted: 23 October 2019 / Published: 25 October 2019
(This article belongs to the Section Engineering Mathematics)
In this paper, we have obtained the prime factorization form of positive integers N for which the number of true different fourth- and fifth-degree permutation polynomials (PPs) modulo N is equal to zero. We have also obtained the prime factorization form of N so that the number of any degree PPs nonreducible at lower degree PPs, fulfilling Zhao and Fan (ZF) sufficient conditions, is equal to zero. Some conclusions are drawn comparing all fourth- and fifth-degree permutation polynomials with those fulfilling ZF sufficient conditions. View Full-Text
Keywords: permutation polynomial; number of PPs equal to 0; Zhao and Fan sufficient conditions permutation polynomial; number of PPs equal to 0; Zhao and Fan sufficient conditions
MDPI and ACS Style

Trifina, L.; Tarniceriu, D. When Is the Number of True Different Permutation Polynomials Equal to 0? Mathematics 2019, 7, 1018.

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