  Let $p$ be a prime and $n$ be a positive integer, and consider
$f_b(X)=X+(X^p-X+b)^{-1}\in \Bbb F_p(X)$, where $b\in\Bbb F_{p^n}$ is such that
$\text{Tr}_{p^n/p}(b)\ne 0$. It is known that (i) $f_b$ permutes $\Bbb F_{p^n}$
for $p=2,3$ and all $n\ge 1$; (ii) for $p>3$ and $n=2$, $f_b$ permutes $\Bbb
F_{p^2}$ if and only if $\text{Tr}_{p^2/p}(b)=\pm 1$; and (iii) for $p>3$ and
$n\ge 5$, $f_b$ does not permute $\Bbb F_{p^n}$. It has been conjectured that
for $p>3$ and $n=3,4$, $f_b$ does not permute $\Bbb F_{p^n}$. We prove this
conjecture for sufficiently large $p$.
