Universal Higher Order Bernoulli Numbers and Kummer and Related Congruences Original Research Article

We define higher or arbitrary order universal Bernoulli numbers and higher order universal Bernoulli–Hurwitz numbers. We deduce a universal first-order Kummer congruence and a congruence for the higher order universal Bernoulli–Hurwitz numbers from Clarkeʹs universal von Staudt theorem. We also establish other Kummer-type congruences for the higher order universal Bernoulli numbers and for the universal Nörlund polynomials, generalizing the authorʹs previous work.