中文摘要：

本文研究平面2N＋1一体问题的周期解，利用Hermite矩阵和循环矩阵的性质。给出了几何中心带一个质量的平面正多边形套问题存在周期解的必要和充分条件，证明了该周期解的存在唯一性，推广了文献[9]的结论。

英文摘要：

In this paper we study periodic solutions of 2N＋1-body problems. Using properties of Hermite matrix and circular matrix, we propose the necessary and sufficient conditions of periodic solutions for the nested regular polygon of planar 2N＋1-body problem with a mass at the geometrical center, and prove the existence and uniqueness of the periodic solutions. This work extends the results in[9].