Abstract In this paper we give some interesting equation of p-adic q-integrals on ℤp. From those p-adic q-integrals, we present a systemic study of some families of extended Carlitz q-Bernoulli ...

Jakob Bernoulli, head of a dynasty of brilliant scholars, was one of the world's leading mathematicians. His great work, Ars Conjectandi, published in 1713, included a profound result that he ...

Jonathan W. Tanner, Samuel S. Wagstaff, Jr. We prove a new congruence for computing Bernoulli numbers modulo a prime. Since it is similar to Vandiver's congruences but has fewer terms, it may be used ...

The Science Quiz appears twice a week in the daily science page. The page is available to read on all days except Saturday in the epaper. Questions (answers at the bottom): 1. The Bernoulli numbers ...

Once upon a time, there lived a family in Switzerland—by the name of Bernoulli. I mention the name because most once-students of science know of it from physics in high-school or early-college years.