数字和以及丢番图m元组等问题的研究

In this project, we mainly research some problems in Number Theory. (1). Sum of digits. (2). Diophantine m-tuples. The applicant of the project have obtained some results on the sum of digits of polynomial values, ordinary integers and the arithmetic progressions in sumsets and difference sets, and published papers in J. Number Theory, Int. J. Number Theory and Integers. .In this project, we should combine techniques of combinatorics and analytical methods to solve problems in Number Theory, and we also should use the theoretical knowledge of elliptic curves to solve the problems of Diophantine m-tuples.

本项目主要研究数论中几个问题：(1) 数字和 。(2)丢番图m-元组。项目申请人已经在多项式值的数字和、平凡数以及和集与差集中的等差数列等方面取得了一些结果，在J. Number Theory, Int. J. Number Theory, Integers等数论专业期刊上发表论文数篇。本项目拟将组合技巧与分析方法相结合来解决数论问题, 还将利用椭圆曲线的相关理论来解决丢番图m元组的问题。