同余式研究具有悠久的历史，很多数学家曾研究过同余式，至今仍有很多人研究该领域。所以同余式研究仍是一个热点课题。.我们将对下面内容进行研究：1）利用Wilf-Zeilberger方法研究Ramanujan型1/π级数的截断同余式，并做到带Euler数或多项式，Bernoulli数或多项式，我们将模更高的素数幂次。2）利用Wilf-Zeilberger方法研究Atkin 和Swinnerton-Dyer超同余式，该途径至今少有使用，我们将丰富研究Atkin 和Swinnerton-Dyer超同余式的方法和工具。3）我们也将研究截断超几何级数的同余式问题，对超几何级数做截断去研究超几何级数的截断同余式和二次变换性质，并试图弄清楚哪些结果与带有复乘的椭圆曲线有关系。.同余式在密码学中有广泛的应用。且它与代数拓扑，椭圆曲线，超几何函数等领域有密切的联系，所以同余式研究具有跨学科的研究价值。

The research of congruences has a long history, and congruences were investigated by lots of people. There are still many people studying this field. So congruence research is still a hot topic.. We will study the following contents: 1) Using the Wilf-Zeilberger method to study truncated congruences of Ramanujan-type 1/πseries, and we will do them with Euler numbers or polynimials, Bernoulli numbers or polynomials,we will modulo higher prime powers. 2) Using the Wilf-Zeilberger method to study Atkin and Swinnerton-Dyer supercongruences, so far, this approach has rarely been tried, so we will enrich the methods and tools for studying Atkin and Swinnerton-Dyer supercongruences. 3) We will also study some new congruences of truncated hypergeometric series, first we truncate some know hypergeometric series, then we study truncated congruences and the properties of quadratic transformation of hypergeometric series, and trying to figure out which results are related to the elliptic curves with complex multiplication.. The application of congruences in cryptography is very extensive. Congruences are also closely related to algebraic topology, elliptic curves, hypergeometric functions and other fields. Therefore, the research of congruences has interdisciplinary value.