Abstract

Let B_{n,k} and A_{n} = ∑_{j=1}^{n} B_{n,j} with A_{0} = 1 be, respectively, the (n, k)^{th} partial and the n^{th} complete Bell polynomials with indeterminate arguments x_{1}, x_{2}, . . .. Congruences for A_{n} and B_{n,k} with respect to a prime number have been studied by several authors. In the present paper, we propose some results involving congruences for B_{n,k} when the arguments are integers. We give a relation between Bell polynomials and we apply it to several congruences. The obtained congruences are connected to binomial coefficients.