Congruences involving Bernoulli numbers and Fermat-Euler quotients.

Let B-m be the mth Bernoulli number in the even suffix notation and let q(a, n) = (a(phi(n)) - 1)/n be the Fermat-Euler quotient, where a, n greater than or equal to 2 are relatively prime positive integers and phi is the Euler totient function. The main purpose of this paper is to devise a certain congruence involving the Bernoulli number and Fermat-Euler quotient, which leads to several important arithmetic properties of Bernoulli numbers. (C) 2002 Elsevier Science (USA).