International Journal of Mathematics and Mathematical Sciences
Volume 13 (1990), Issue 2, Pages 337-342
doi:10.1155/S0161171290000497
Abstract
A polynomial f over a finite feld F is a permutation polynomial if the mapping F→F defined by f is one-to-one. We are concerned here with binomials, that is, polynomials of the shape f=aXi+bXj+c, i>j≥1. Even in this restricted setting, it is impossible to give general necessary and sufficient conditions on a, b, c for f to be a permutation polynomial. We review, and systematize, what is known.