对组合数论的研究已经有相当长的历史，但是至今仍然非常活跃，此领域中的经典、热点问题不胜枚举。本项目主要将概率的方法应用到组合数论的研究中，在已有工作的基础上，争取解决一些问题并得到一些新的结果。具体的，我们首先计划研究素数的加法补集，在研究此问题的过程中，我们争取得到概率中的著名的Janson不等式的推广形式。其次，我们计划研究Erdos-Fuchs问题及其反问题。此外，我们还将对奇完全数、多重奇完全数，以及和集问题进行研究。

The research of combinatorial number theory has a long history,but it is still very active. In this projects ,based on the existing work,we plan to use probabilistic methods to solve some problems in combinatorial number theory and get some new results.Firstly, we shall study the additive complements of primes by the probabilistic methods which is a new tool to be used widely in the research on this subject. In addition, we try to generalize a probabilistic inequality of Janson.Secondly, the Erdos-Fuch problem and its inverse problem have been studied for many years. Authors presented various versions of the theorem. We shall study the quantitative Erdős-Fuchs theorem, its generalization and its inverse problem for k-fold sumsets.Finally we will try to give some new properties of odd perfect numbers,odd multiperfect numbers and sumsets.