  Let $\underline{a}$ and $\underline{b}$ be primitive sequences over
$\mathbb{Z}/(p^e)$ with odd prime $p$ and $e\ge 2$. For certain compressing
maps, we consider the distribution properties of compressing sequences of
$\underline{a}$ and $\underline{b}$, and prove that
$\underline{a}=\underline{b}$ if the compressing sequences are equal at the
times $t$ such that $\alpha(t)=k$, where $\underline{\alpha}$ is a sequence
related to $\underline{a}$. We also discuss the $s$-uniform distribution
property of compressing sequences. For some compressing maps, we have that
there exist different primitive sequences such that the compressing sequences
are $s$-uniform. We also discuss that compressing sequences can be $s$-uniform
for how many elements $s$.
