Geodesic
Dickson Polynomials of the Second Kind that are Permutations
Canadian journal of mathematics, Tome 46 (1994) no. 2, pp. 225-238

Voir la notice de l'article provenant de la source Cambridge University Press

It is known that the Dickson polynomial of the second kind permutes the elements of the finite prime field (p odd) when n + 1 = ±2 to each of the moduli and . Based on numerical evidence it has been conjectured that these congruences are necessary for the polynomial to permute . The conjecture is established here by a new method
DOI : 10.4153/CJM-1994-009-8
Mots-clés : 11T06 
Cohen, Stephen D. Dickson Polynomials of the Second Kind that are Permutations. Canadian journal of mathematics, Tome 46 (1994) no. 2, pp. 225-238. doi: 10.4153/CJM-1994-009-8
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[1] 1. Brison, O. J., On group permutation polynomials, Portugal. Math. 50(1993), 365–383. Google Scholar

[2] 2. Fried, M. and Lidl, R., On Dickson polynomials and Rédei functions, Proc. Salzburg Conf., Contributions to General Algebra 5, Springer-Verlag Holder-Pichler-Tempsky, Wien, 1987, 139–149. Google Scholar

[3] 3. James, N. S. and Lidl, R., Permutation polynomials on matrices, Linear Algebra Appl. 96(1987), 181–190. Google Scholar

[4] 4. Lidl, R. and Mullen, G. L., When does a polynomial over a finite field permute the elements of the field?, Amer. Math. Monthly 95(1988), 243–246. Google Scholar

[5] 5. Lidl, R. and Niederreiter, H., Finite Fields, Encyclo. Math. Appls. 20, Addison-Wesley, Reading, Massachusetts, 1983. Google Scholar

[6] 6. Matthews, R. W., Permutation polynomials in one and several variables, Ph.D. Dissertation, University of Tasmania, 1982. Google Scholar

[7] 7. Mullen, G. L., Dickson polynomials over finite fields, Adv. in Math. (Beijing) 20(1991), 24–32. Google Scholar

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