On Kummer-Type Congruences for Derivatives of Barnesʹ Multiple Bernoulli Polynomials Original Research Article

The theorem of Kummer congruences of Bernoulli numbers says that if p−1does not dividem and m≡n (mod pN(p−1)), thenimage In this paper we generalize these congruences to derivatives of Barnesʹ multiple Bernoulli polynomials by an elementary method and give a p-adic interpretation of them.