on a conjecture on permutation rational functions over finite fields

Daniele Bartoli, Xiang-dong Hou

Let $p$ be a prime and $n$ be a positive integer, and consider $f_b(X)=X+(X^p-X+b{)}^{-1}\in {\mathbb{F}}_p(X)$, where $b\in {\mathbb{F}}_{p^n}$ is such that ${\text{Tr}}_{p^n/p}(b)\ne 0$. It is kn…