  In this paper, we study a class $\mathcal{A}(\lambda ,n,m)$ of self-similar
sets with $m$ exact overlaps generated by $n$ similitudes of the same ratio $
\lambda $. We obtain a necessary condition for a self-similar set in
$\mathcal{A}(\lambda ,n,m)$ to be Lipschitz equivalent to a self-similar set
satisfying the strong separation condition, i.e., there exists an integer $
k\geq 2$ such that $x^{2k}-mx^{k}+n$ is reducible, in particular, $m$ belongs
to $\{a^{i}:a\in \mathbb{N}$ with $i\geq 2\}.$
