Congruences ofp-adic Integer Order Bernoulli Numbers Original Research Article

In this paper we establish some new congruences ofp-adic integer order Bernoulli numbers. These generalize the Kummer congruences for ordinary Bernoulli numbers. We apply our congruences to prove irreducibility of certain Bernoulli polynomials with order divisible bypand to get new congruences for Stirling numbers.