By means of simple identities among rational functions of a particular type, we are able to produce identities among Bernoulli numbers and from them congruences of the form.
when the odd prime p has the property that p-1 is not a divisor of the positive even integer m. With such relations, we are able to produce new identities among Bernoulli numbers as well as reproving congruences of Kummer type such as
when ω is a multiple of (p-1)pe-1, e ≥ 1.
@article{1700,
title = {A new approach to congruences of Kummer type for Bernoulli numbers},
journal = {CUBO, A Mathematical Journal},
volume = {5},
year = {2003},
language = {en},
url = {http://dml.mathdoc.fr/item/1700}
}
Eie, Minking; Lin Ong, Yao. A new approach to congruences of Kummer type for Bernoulli numbers. CUBO, A Mathematical Journal, Tome 5 (2003) 16 p. http://gdmltest.u-ga.fr/item/1700/