论文标题
一些涉及广义Bernoulli数字和Bernoulli多项式的一致性
Some congruences involving generalized Bernoulli numbers and Bernoulli polynomials
论文作者
论文摘要
令$ [x] $为$ x $，$ n> 1 $的组成部分，为正整数，$χ_n$表示琐碎的dirichlet角色modulo $ n $。在本文中，我们使用Z. H. Sun建立的身份来获得$ t_ {m，k}（n）= \ sum_ {x = 1}^{[n/m]} \ frac {χ_n（X）} \ {1,2 \} $，$ n \ equiv \ pm 1 \ left的任何正整数$ m $（\ bmod m \ right）$在bernoulli polyenmials方面。作为一个应用程序，我们还获得了一些新的一致性，涉及二项式系数Modulo $ n^4 $，就广义伯努利数字而言。
Let $[x]$ be the integral part of $x$, $n>1$ be a positive integer and $χ_n$ denote the trivial Dirichlet character modulo $n$. In this paper, we use an identity established by Z. H. Sun to get congruences of $T_{m,k}(n)=\sum_{x=1}^{[n/m]}\frac{χ_n(x)}{x^k}\left(\bmod n^{r+1}\right)$ for $r\in \{1,2\}$, any positive integer $m $ with $n \equiv \pm 1 \left(\bmod m \right)$ in terms of Bernoulli polynomials. As its an application, we also obtain some new congruences involving binomial coefficients modulo $n^4$ in terms of generalized Bernoulli numbers.
