Bernoulli Polynomials and Their Some New Congruence Properties

Abstract

The aim of this article is to use the fundamental modus and the properties of the Euler polynomials and Bernoulli polynomials to prove some new congruences related to Bernoulli polynomials. One of them is that for any integer h or any non-negative integer n, we obtain the congruence B 2 n + 1 ( 2 h ) ≡ 0 mod ( 2 n + 1 ) , where B n ( x ) are Bernoulli polynomials.