Bounds of divided universal Bernoulli numbers and universal Kummer congruences

Let p be a prime. We obtain good bounds for the p-adic sizes of the coefficients of the divided universal Bernoulli number (B) over cap (n)/n when n is divisible by p - 1. As an application, we give a simple proof of Clarke's 1989 universal von Staudt theorem. We also establish the universal Kummer congruences modulo p for the divided universal Bernoulli numbers for the case (p - 1)vertical bar n, which is a new result.