Congruences Involving Bernoulli Numbers and Fermat–Euler Quotients Original Research Article

Let Bm be the mth Bernoulli number in the even suffix notation and let q(a, n)=(aphi(n)−1)/n be the Fermat–Euler quotient, where a, ngreater-or-equal, slanted2 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.