本项目主要研究Erdos-Turan 猜想、Sarkozy 教授提出的表示函数问题以及加法补问题。运用Single 引理、有限域理论、生成函数方法等分析研究Erdos-Turan 猜想以及与其相关的一些问题；运用指数和方法以及一些组合方法研究表示函数问题，该问题包括整数分拆情形以及模m循环群的分拆情形；采用分圆多项式理论及一些组合方法对一些加法补问题进行研究。

In this project, we mainly study the Erdos-Turan conjecture, representation function problems posed by Sarkozy, and some problems of additive complements. First, we study the Erdos-Turan conjecture and some related problems by using Single's lemma, the theory of finite fields, generating functions, and so on. Next, using exponential sum and some combinatorial methods, we study representation function problems, including cases of partitions of natural numbers and partitions of cyclic groups modulo m. Finally, we study some problems related to additive complements by using the theory of cyclotomic polynomials and some combinatorial methods.