  We show that for each $n \geq 2$, the systoles of closed hyperbolic
$n$-manifolds form a dense subset of $(0, +\infty)$. We also show that for any
$n\geq 2$ and any Salem number $\lambda$, there is a closed arithmetic
hyperbolic $n$-manifold of systole $\log(\lambda)$. In particular, the Salem
conjecture holds if and only if the systoles of closed arithmetic hyperbolic
manifolds in some (any) dimension fail to be dense in $(0, +\infty)$.
