Permutation binomials
Charles Small · International Journal of Mathematics and Mathematical Sciences · 1988
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.