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

Lucian Trifina and Daniela Tarniceriu
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Lucian Trifina: Department of Telecommunications and Information Technologies, “Gheorghe Asachi” Technical University, Iasi 700506, Romania
Daniela Tarniceriu: Department of Telecommunications and Information Technologies, “Gheorghe Asachi” Technical University, Iasi 700506, Romania

Mathematics, 2019, vol. 7, issue 11, 1-14

Abstract: 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.

Keywords: permutation polynomial; number of PPs equal to 0; Zhao and Fan sufficient conditions (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
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