Mollin, R. A.Small, C.2018-09-272018-09-271987-01-01R. A. Mollin and C. Small, “On permutation polynomials over finite fields,” International Journal of Mathematics and Mathematical Sciences, vol. 10, no. 3, pp. 535-543, 1987. doi:10.1155/S0161171287000644http://hdl.handle.net/1880/108670https://doi.org/10.11575/PRISM/44629A polynomial f over a finite field F is called a permutation polynomial if the mapping F→F defined by f is one-to-one. In this paper we consider the problem of characterizing permutation polynomials; that is, we seek conditions on the coefficients of a polynomial which are necessary and sufficient for it to represent a permutation. We also give some results bearing on a conjecture of Carlitz which says essentially that for any even integer m, the cardinality of finite fields admitting permutation polynomials of degree m is bounded.Journal Article2018-09-27enCopyright © 1987 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.https://doi.org/10.1155/S0161171287000644