3-adic同余式与关于Catalan数的同余式

我们主要研究关于中心二项式系数、Apéry数及Franel数的和式的3-adic同余式，以及关于Catalan数或高阶Catalan数模奇素数或者奇素数平方的同余式。希望通过此项目的研究在几个相关同余式的猜想方面取得突破性进展乃至完全解决。

We plan to study some congruences related to 3-adic valuations of sums involving central binomial coefficients、Apéry numbers and Franel numbers.We will also investigate congruences on Catalan numbers or higher-order Catalan numbers modulo an odd prime p or the square of an odd prime p .We hope to make substantial progress on several related conjectures or even solve some of them completely.