A congruence involving the quotients of Euler and its applications (III)

TL;DR

This paper presents new congruences involving binomial coefficients modulo integers, extending previous work by Cai et al., and explores their mathematical applications.

Contribution

It introduces novel congruences related to Euler's quotients, advancing the theoretical understanding of binomial coefficients in modular arithmetic.

Findings

New congruences involving binomial coefficients under integer moduli

Extensions of previous results by Cai et al.

Potential applications in number theory and combinatorics

Abstract

In this paper, we will present several new congruences involving binomial coefficients under integer moduli, which are the continuation of the previous two work by Cai \textit{et al.} (2002, 2007).